diff --git a/core/src/main/scala-2.12-/cats/instances/all.scala b/core/src/main/scala-2.12-/cats/instances/all.scala
index 02dddee872..b67a56c8ac 100644
--- a/core/src/main/scala-2.12-/cats/instances/all.scala
+++ b/core/src/main/scala-2.12-/cats/instances/all.scala
@@ -50,3 +50,5 @@ private[cats] trait AllInstancesBinCompat3 extends AllCoreDurationInstances
 private[cats] trait AllInstancesBinCompat4 extends SortedMapInstancesBinCompat1 with MapInstancesBinCompat1
 
 private[cats] trait AllInstancesBinCompat5 extends SortedSetInstancesBinCompat0
+
+private[cats] trait AllInstancesBinCompat6 extends SortedSetInstancesBinCompat1 with SortedMapInstancesBinCompat2
diff --git a/core/src/main/scala-2.12-/cats/instances/package.scala b/core/src/main/scala-2.12-/cats/instances/package.scala
index c171490fbb..0805b3ad56 100644
--- a/core/src/main/scala-2.12-/cats/instances/package.scala
+++ b/core/src/main/scala-2.12-/cats/instances/package.scala
@@ -9,6 +9,7 @@ package object instances {
       with AllInstancesBinCompat3
       with AllInstancesBinCompat4
       with AllInstancesBinCompat5
+      with AllInstancesBinCompat6
   object bigInt extends BigIntInstances
   object bigDecimal extends BigDecimalInstances
   object bitSet extends BitSetInstances
@@ -38,8 +39,12 @@ package object instances {
   object queue extends QueueInstances
   object set extends SetInstances
   object short extends ShortInstances
-  object sortedMap extends SortedMapInstances with SortedMapInstancesBinCompat0 with SortedMapInstancesBinCompat1
-  object sortedSet extends SortedSetInstances with SortedSetInstancesBinCompat0
+  object sortedMap
+      extends SortedMapInstances
+      with SortedMapInstancesBinCompat0
+      with SortedMapInstancesBinCompat1
+      with SortedMapInstancesBinCompat2
+  object sortedSet extends SortedSetInstances with SortedSetInstancesBinCompat0 with SortedSetInstancesBinCompat1
   object stream extends StreamInstances with StreamInstancesBinCompat0
   object string extends StringInstances
   object try_ extends TryInstances
diff --git a/core/src/main/scala-2.13+/cats/instances/all.scala b/core/src/main/scala-2.13+/cats/instances/all.scala
index b0220e3ee4..9524d80617 100644
--- a/core/src/main/scala-2.13+/cats/instances/all.scala
+++ b/core/src/main/scala-2.13+/cats/instances/all.scala
@@ -51,3 +51,5 @@ private[cats] trait AllInstancesBinCompat3 extends AllCoreDurationInstances
 private[cats] trait AllInstancesBinCompat4 extends SortedMapInstancesBinCompat1 with MapInstancesBinCompat1
 
 private[cats] trait AllInstancesBinCompat5 extends SortedSetInstancesBinCompat0
+
+private[cats] trait AllInstancesBinCompat6 extends SortedSetInstancesBinCompat1 with SortedMapInstancesBinCompat2
diff --git a/core/src/main/scala-2.13+/cats/instances/package.scala b/core/src/main/scala-2.13+/cats/instances/package.scala
index fa49782947..6fb10eec1f 100644
--- a/core/src/main/scala-2.13+/cats/instances/package.scala
+++ b/core/src/main/scala-2.13+/cats/instances/package.scala
@@ -9,6 +9,7 @@ package object instances {
       with AllInstancesBinCompat3
       with AllInstancesBinCompat4
       with AllInstancesBinCompat5
+      with AllInstancesBinCompat6
   object bigInt extends BigIntInstances
   object bigDecimal extends BigDecimalInstances
   object bitSet extends BitSetInstances
@@ -38,8 +39,12 @@ package object instances {
   object queue extends QueueInstances
   object set extends SetInstances
   object short extends ShortInstances
-  object sortedMap extends SortedMapInstances with SortedMapInstancesBinCompat0 with SortedMapInstancesBinCompat1
-  object sortedSet extends SortedSetInstances with SortedSetInstancesBinCompat0
+  object sortedMap
+      extends SortedMapInstances
+      with SortedMapInstancesBinCompat0
+      with SortedMapInstancesBinCompat1
+      with SortedMapInstancesBinCompat2
+  object sortedSet extends SortedSetInstances with SortedSetInstancesBinCompat0 with SortedSetInstancesBinCompat1
 
   @deprecated("2.0.0-RC2", "Use cats.instances.lazyList")
   object stream extends StreamInstances with StreamInstancesBinCompat0
diff --git a/core/src/main/scala/cats/instances/sortedMap.scala b/core/src/main/scala/cats/instances/sortedMap.scala
index 555dcf04a4..8ed33c47d7 100644
--- a/core/src/main/scala/cats/instances/sortedMap.scala
+++ b/core/src/main/scala/cats/instances/sortedMap.scala
@@ -2,19 +2,19 @@ package cats.instances
 
 import cats.{Always, Applicative, Eval, FlatMap, Foldable, Monoid, MonoidK, Order, Show, Traverse, TraverseFilter}
 import cats.kernel._
-import cats.kernel.instances.StaticMethods
 
 import scala.annotation.tailrec
 import scala.collection.immutable.SortedMap
 
 trait SortedMapInstances extends SortedMapInstances2 {
 
-  implicit def catsStdHashForSortedMap[K: Hash: Order, V: Hash]: Hash[SortedMap[K, V]] =
-    new SortedMapHash[K, V]
+  @deprecated("2.0.0-RC2", "Use cats.kernel.instances.sortedMap.catsKernelStdHashForSortedMap")
+  private[instances] def catsStdHashForSortedMap[K: Hash: Order, V: Hash]: Hash[SortedMap[K, V]] =
+    cats.kernel.instances.sortedMap.catsKernelStdHashForSortedMap[K, V]
 
-  implicit def catsStdCommutativeMonoidForSortedMap[K: Order, V: CommutativeSemigroup]
-    : CommutativeMonoid[SortedMap[K, V]] =
-    new SortedMapCommutativeMonoid[K, V]
+  @deprecated("2.0.0-RC2", "Use cats.kernel.instances.sortedMap.catsKernelStdCommutativeMonoidForSortedMap")
+  private[instances] def catsStdCommutativeMonoidForSortedMap[K: Order, V: CommutativeSemigroup] =
+    cats.kernel.instances.sortedMap.catsKernelStdCommutativeMonoidForSortedMap[K, V]
 
   implicit def catsStdShowForSortedMap[A: Order, B](implicit showA: Show[A], showB: Show[B]): Show[SortedMap[A, B]] =
     new Show[SortedMap[A, B]] {
@@ -114,76 +114,39 @@ trait SortedMapInstances extends SortedMapInstances2 {
 }
 
 private[instances] trait SortedMapInstances1 {
-  implicit def catsStdEqForSortedMap[K: Order, V: Eq]: Eq[SortedMap[K, V]] =
+  @deprecated("2.0.0-RC2", "Use cats.kernel.instances.sortedMap.catsKernelStdEqForSortedMap")
+  private[instances] def catsStdEqForSortedMap[K: Order, V: Eq]: Eq[SortedMap[K, V]] =
     new SortedMapEq[K, V]
 }
 
 private[instances] trait SortedMapInstances2 extends SortedMapInstances1 {
-  implicit def catsStdMonoidForSortedMap[K: Order, V: Semigroup]: Monoid[SortedMap[K, V]] =
+  @deprecated("2.0.0-RC2", "Use cats.kernel.instances.sortedMap.catsKernelStdMonoidForSortedMap")
+  private[instances] def catsStdMonoidForSortedMap[K: Order, V: Semigroup]: Monoid[SortedMap[K, V]] =
     new SortedMapMonoid[K, V]
 }
 
+@deprecated("2.0.0-RC2", "Use cats.kernel.instances.SortedMapHash")
 class SortedMapHash[K, V](implicit V: Hash[V], O: Order[K], K: Hash[K])
-    extends SortedMapEq[K, V]()(V, O)
+    extends SortedMapEq[K, V]
     with Hash[SortedMap[K, V]] {
-  // adapted from [[scala.util.hashing.MurmurHash3]],
-  // but modified standard `Any#hashCode` to `ev.hash`.
-  import scala.util.hashing.MurmurHash3._
-  def hash(x: SortedMap[K, V]): Int = {
-    var a, b, n = 0
-    var c = 1
-    x.foreach {
-      case (k, v) =>
-        val h = StaticMethods.product2HashWithPrefix(K.hash(k), V.hash(v), "Tuple2")
-        a += h
-        b ^= h
-        c = StaticMethods.updateUnorderedHashC(c, h)
-        n += 1
-    }
-    var h = mapSeed
-    h = mix(h, a)
-    h = mix(h, b)
-    h = mixLast(h, c)
-    finalizeHash(h, n)
-  }
+  private[this] val underlying: Hash[SortedMap[K, V]] = new cats.kernel.instances.SortedMapHash[K, V]
+  def hash(x: SortedMap[K, V]): Int = underlying.hash(x)
 }
 
-class SortedMapEq[K, V](implicit V: Eq[V], O: Order[K]) extends Eq[SortedMap[K, V]] {
-  def eqv(x: SortedMap[K, V], y: SortedMap[K, V]): Boolean =
-    if (x eq y) true
-    else
-      x.size == y.size && x.forall {
-        case (k, v1) =>
-          y.get(k) match {
-            case Some(v2) => V.eqv(v1, v2)
-            case None     => false
-          }
-      }
-}
+@deprecated("2.0.0-RC2", "Use cats.kernel.instances.SortedMapEq")
+class SortedMapEq[K, V](implicit V: Eq[V], O: Order[K]) extends cats.kernel.instances.SortedMapEq[K, V]
 
+@deprecated("2.0.0-RC2", "Use cats.kernel.instances.SortedMapCommutativeMonoid")
 class SortedMapCommutativeMonoid[K, V](implicit V: CommutativeSemigroup[V], O: Order[K])
     extends SortedMapMonoid[K, V]
-    with CommutativeMonoid[SortedMap[K, V]]
-
-class SortedMapMonoid[K, V](implicit V: Semigroup[V], O: Order[K]) extends Monoid[SortedMap[K, V]] {
-
-  def empty: SortedMap[K, V] = SortedMap.empty(O.toOrdering)
-
-  def combine(xs: SortedMap[K, V], ys: SortedMap[K, V]): SortedMap[K, V] =
-    if (xs.size <= ys.size) {
-      xs.foldLeft(ys) {
-        case (my, (k, x)) =>
-          my.updated(k, Semigroup.maybeCombine(x, my.get(k)))
-      }
-    } else {
-      ys.foldLeft(xs) {
-        case (mx, (k, y)) =>
-          mx.updated(k, Semigroup.maybeCombine(mx.get(k), y))
-      }
-    }
-
+    with CommutativeMonoid[SortedMap[K, V]] {
+  private[this] val underlying: CommutativeMonoid[SortedMap[K, V]] =
+    new cats.kernel.instances.SortedMapCommutativeMonoid[K, V]
 }
 
+@deprecated("2.0.0-RC2", "Use cats.kernel.instances.SortedMapMonoid")
+class SortedMapMonoid[K, V](implicit V: Semigroup[V], O: Order[K]) extends cats.kernel.instances.SortedMapMonoid[K, V]
+
 private[instances] trait SortedMapInstancesBinCompat0 {
   implicit def catsStdTraverseFilterForSortedMap[K: Order]: TraverseFilter[SortedMap[K, *]] =
     new TraverseFilter[SortedMap[K, *]] {
@@ -231,3 +194,5 @@ private[instances] trait SortedMapInstancesBinCompat1 {
     override def combineK[A](x: SortedMap[K, A], y: SortedMap[K, A]): SortedMap[K, A] = x ++ y
   }
 }
+
+private[instances] trait SortedMapInstancesBinCompat2 extends cats.kernel.instances.SortedMapInstances
diff --git a/core/src/main/scala/cats/instances/sortedSet.scala b/core/src/main/scala/cats/instances/sortedSet.scala
index 0855b8d3d6..7f55f58fe3 100644
--- a/core/src/main/scala/cats/instances/sortedSet.scala
+++ b/core/src/main/scala/cats/instances/sortedSet.scala
@@ -2,10 +2,8 @@ package cats
 package instances
 
 import cats.kernel.{BoundedSemilattice, Hash, Order}
-import cats.kernel.instances.StaticMethods
 import scala.collection.immutable.SortedSet
 import scala.annotation.tailrec
-import cats.implicits._
 
 trait SortedSetInstances extends SortedSetInstances1 {
 
@@ -64,19 +62,22 @@ trait SortedSetInstances extends SortedSetInstances1 {
 
   implicit def catsStdShowForSortedSet[A: Show]: Show[SortedSet[A]] = new Show[SortedSet[A]] {
     def show(fa: SortedSet[A]): String =
-      fa.iterator.map(_.show).mkString("SortedSet(", ", ", ")")
+      fa.iterator.map(Show[A].show).mkString("SortedSet(", ", ", ")")
   }
 
-  implicit def catsKernelStdOrderForSortedSet[A: Order]: Order[SortedSet[A]] =
-    new SortedSetOrder[A]
+  @deprecated("2.0.0-RC2", "Use cats.kernel.instances.sortedSet.catsKernelStdOrderForSortedSet")
+  private[instances] def catsKernelStdOrderForSortedSet[A: Order]: Order[SortedSet[A]] =
+    cats.kernel.instances.sortedSet.catsKernelStdOrderForSortedSet[A]
 }
 
 private[instances] trait SortedSetInstances1 {
-  implicit def catsKernelStdHashForSortedSet[A: Order: Hash]: Hash[SortedSet[A]] =
-    new SortedSetHash[A]
+  @deprecated("2.0.0-RC2", "Use cats.kernel.instances.sortedSet.catsKernelStdHashForSortedSet")
+  private[instances] def catsKernelStdHashForSortedSet[A: Order: Hash]: Hash[SortedSet[A]] =
+    cats.kernel.instances.sortedSet.catsKernelStdHashForSortedSet[A]
 
-  implicit def catsKernelStdSemilatticeForSortedSet[A: Order]: BoundedSemilattice[SortedSet[A]] =
-    new SortedSetSemilattice[A]
+  @deprecated("2.0.0-RC2", "Use cats.kernel.instances.sortedSet.catsKernelStdSemilatticeForSortedSet")
+  private[instances] def catsKernelStdSemilatticeForSortedSet[A: Order]: BoundedSemilattice[SortedSet[A]] =
+    cats.kernel.instances.sortedSet.catsKernelStdBoundedSemilatticeForSortedSet[A]
 }
 
 private[instances] trait SortedSetInstancesBinCompat0 {
@@ -90,43 +91,27 @@ private[instances] trait SortedSetInstancesBinCompat0 {
   }
 }
 
-class SortedSetOrder[A: Order] extends Order[SortedSet[A]] {
-  def compare(a1: SortedSet[A], a2: SortedSet[A]): Int =
-    Order[Int].compare(a1.size, a2.size) match {
-      case 0 => StaticMethods.iteratorCompare(a1.iterator, a2.iterator)
-      case x => x
-    }
-
-  override def eqv(s1: SortedSet[A], s2: SortedSet[A]): Boolean =
-    StaticMethods.iteratorEq(s1.iterator, s2.iterator)
+private[instances] trait SortedSetInstancesBinCompat1 extends LowPrioritySortedSetInstancesBinCompat1 {
+  // TODO: Remove when this is no longer necessary for binary compatibility.
+  implicit override def catsKernelStdHashForSortedSet[A: Order: Hash]: Hash[SortedSet[A]] =
+    cats.kernel.instances.sortedSet.catsKernelStdHashForSortedSet[A]
 }
 
-class SortedSetHash[A: Order: Hash] extends Hash[SortedSet[A]] {
-  import scala.util.hashing.MurmurHash3._
-
-  // adapted from [[scala.util.hashing.MurmurHash3]],
-  // but modified standard `Any#hashCode` to `ev.hash`.
-  def hash(xs: SortedSet[A]): Int = {
-    var a, b, n = 0
-    var c = 1
-    xs.foreach { x =>
-      val h = Hash[A].hash(x)
-      a += h
-      b ^= h
-      c = cats.kernel.instances.StaticMethods.updateUnorderedHashC(c, h)
-      n += 1
-    }
-    var h = setSeed
-    h = mix(h, a)
-    h = mix(h, b)
-    h = mixLast(h, c)
-    finalizeHash(h, n)
-  }
-  override def eqv(s1: SortedSet[A], s2: SortedSet[A]): Boolean =
-    StaticMethods.iteratorEq(s1.iterator, s2.iterator)(Order[A])
-}
+private[instances] trait LowPrioritySortedSetInstancesBinCompat1
+    extends cats.kernel.instances.SortedSetInstances
+    with SortedSetInstances {
+  implicit override def catsKernelStdOrderForSortedSet[A: Order]: Order[SortedSet[A]] =
+    cats.kernel.instances.sortedSet.catsKernelStdOrderForSortedSet[A]
 
-class SortedSetSemilattice[A: Order] extends BoundedSemilattice[SortedSet[A]] {
-  def empty: SortedSet[A] = SortedSet.empty(implicitly[Order[A]].toOrdering)
-  def combine(x: SortedSet[A], y: SortedSet[A]): SortedSet[A] = x | y
+  override def catsKernelStdHashForSortedSet[A: Order: Hash]: Hash[SortedSet[A]] =
+    cats.kernel.instances.sortedSet.catsKernelStdHashForSortedSet[A]
 }
+
+@deprecated("2.0.0-RC2", "Use cats.kernel.instances.SortedSetHash")
+class SortedSetHash[A: Order: Hash] extends cats.kernel.instances.SortedSetHash[A]
+
+@deprecated("2.0.0-RC2", "Use cats.kernel.instances.SortedSetOrder")
+class SortedSetOrder[A: Order] extends cats.kernel.instances.SortedSetOrder[A]
+
+@deprecated("2.0.0-RC2", "Use cats.kernel.instances.SortedSetSemilattice")
+class SortedSetSemilattice[A: Order] extends cats.kernel.instances.SortedSetSemilattice[A]
diff --git a/kernel-laws/shared/src/test/scala/cats/kernel/laws/LawTests.scala b/kernel-laws/shared/src/test/scala/cats/kernel/laws/LawTests.scala
index 59d0bc2c81..f12376e63f 100644
--- a/kernel-laws/shared/src/test/scala/cats/kernel/laws/LawTests.scala
+++ b/kernel-laws/shared/src/test/scala/cats/kernel/laws/LawTests.scala
@@ -12,7 +12,7 @@ import org.scalactic.anyvals.{PosInt, PosZInt}
 import org.scalatest.funsuite.AnyFunSuiteLike
 
 import scala.concurrent.duration.{Duration, FiniteDuration}
-import scala.collection.immutable.{BitSet, Queue}
+import scala.collection.immutable.{BitSet, Queue, SortedMap, SortedSet}
 import scala.util.Random
 import java.util.UUID
 import java.util.concurrent.TimeUnit.{DAYS, HOURS, MICROSECONDS, MILLISECONDS, MINUTES, NANOSECONDS, SECONDS}
@@ -64,6 +64,28 @@ object KernelCheck {
     )
   }
 
+  // Copied from cats-laws.
+  implicit def arbitrarySortedMap[K: Arbitrary: Order, V: Arbitrary]: Arbitrary[SortedMap[K, V]] =
+    Arbitrary(arbitrary[Map[K, V]].map(s => SortedMap.empty[K, V](implicitly[Order[K]].toOrdering) ++ s))
+
+  // Copied from cats-laws.
+  implicit def cogenSortedMap[K: Order: Cogen, V: Cogen]: Cogen[SortedMap[K, V]] = {
+    implicit val orderingK = Order[K].toOrdering
+
+    implicitly[Cogen[Map[K, V]]].contramap(_.toMap)
+  }
+
+  // Copied from cats-laws.
+  implicit def arbitrarySortedSet[A: Arbitrary: Order]: Arbitrary[SortedSet[A]] =
+    Arbitrary(arbitrary[Set[A]].map(s => SortedSet.empty[A](implicitly[Order[A]].toOrdering) ++ s))
+
+  // Copied from cats-laws.
+  implicit def cogenSortedSet[A: Order: Cogen]: Cogen[SortedSet[A]] = {
+    implicit val orderingA = Order[A].toOrdering
+
+    implicitly[Cogen[Set[A]]].contramap(_.toSet)
+  }
+
   // this instance is not available in ScalaCheck 1.13.2.
   // remove this once a newer version is available.
   implicit val cogenBigInt: Cogen[BigInt] =
@@ -127,6 +149,7 @@ class Tests extends AnyFunSuiteLike with Discipline with ScalaVersionSpecificTes
     // needed for Cogen[Map[...]]
     implicit val ohe: Ordering[HasEq[Int]] = Ordering.by[HasEq[Int], Int](_.a)
     checkAll("Eq[Map[String, HasEq[Int]]]", EqTests[Map[String, HasEq[Int]]].eqv)
+    checkAll("Eq[SortedMap[String, HasEq[Int]]]", EqTests[SortedMap[String, HasEq[Int]]].eqv)
   }
 
   checkAll("Eq[List[HasEq[Int]]]", EqTests[List[HasEq[Int]]].eqv)
@@ -172,6 +195,7 @@ class Tests extends AnyFunSuiteLike with Discipline with ScalaVersionSpecificTes
   checkAll("Order[Vector[Int]]", OrderTests[Vector[Int]].order)
   checkAll("Order[Stream[Int]]", OrderTests[Stream[Int]].order)
   checkAll("Order[Queue[Int]]", OrderTests[Queue[Int]].order)
+  checkAll("Order[SortedSet[String]", OrderTests[SortedSet[String]].order)
   checkAll("fromOrdering[Int]", OrderTests(Order.fromOrdering[Int]).order)
   checkAll("Order.reverse(Order[Int])", OrderTests(Order.reverse(Order[Int])).order)
   checkAll("Order.reverse(Order.reverse(Order[Int]))", OrderTests(Order.reverse(Order.reverse(Order[Int]))).order)
@@ -217,16 +241,24 @@ class Tests extends AnyFunSuiteLike with Discipline with ScalaVersionSpecificTes
   checkAll("Monoid[List[String]]", SerializableTests.serializable(Monoid[List[String]]))
   checkAll("Monoid[Map[String, String]]", MonoidTests[Map[String, String]].monoid)
   checkAll("Monoid[Map[String, String]]", SerializableTests.serializable(Monoid[Map[String, String]]))
+  checkAll("Monoid[SortedMap[String, String]]", MonoidTests[SortedMap[String, String]].monoid)
+  checkAll("Monoid[SortedMap[String, String]]", SerializableTests.serializable(Monoid[SortedMap[String, String]]))
   checkAll("Monoid[Queue[Int]]", MonoidTests[Queue[Int]].monoid)
   checkAll("Monoid[Queue[Int]]", SerializableTests.serializable(Monoid[Queue[Int]]))
 
   checkAll("CommutativeMonoid[Map[String, Int]]", CommutativeMonoidTests[Map[String, Int]].commutativeMonoid)
   checkAll("CommutativeMonoid[Map[String, Int]]", SerializableTests.serializable(CommutativeMonoid[Map[String, Int]]))
+  checkAll("CommutativeMonoid[SortedMap[String, Int]]",
+           CommutativeMonoidTests[SortedMap[String, Int]].commutativeMonoid)
+  checkAll("CommutativeMonoid[SortedMap[String, Int]]",
+           SerializableTests.serializable(CommutativeMonoid[SortedMap[String, Int]]))
 
   checkAll("BoundedSemilattice[BitSet]", BoundedSemilatticeTests[BitSet].boundedSemilattice)
   checkAll("BoundedSemilattice[BitSet]", SerializableTests.serializable(BoundedSemilattice[BitSet]))
   checkAll("BoundedSemilattice[Set[Int]]", BoundedSemilatticeTests[Set[Int]].boundedSemilattice)
   checkAll("BoundedSemilattice[Set[Int]]", SerializableTests.serializable(BoundedSemilattice[Set[Int]]))
+  checkAll("BoundedSemilattice[SortedSet[Int]]", BoundedSemilatticeTests[SortedSet[Int]].boundedSemilattice)
+  checkAll("BoundedSemilattice[SortedSet[Int]]", SerializableTests.serializable(BoundedSemilattice[SortedSet[Int]]))
 
   checkAll("CommutativeGroup[Unit]", CommutativeGroupTests[Unit].commutativeGroup)
   checkAll("CommutativeGroup[Unit]", SerializableTests.serializable(CommutativeGroup[Unit]))
@@ -275,6 +307,7 @@ class Tests extends AnyFunSuiteLike with Discipline with ScalaVersionSpecificTes
   checkAll("Hash[(Int, String)]", HashTests[(Int, String)].hash)
   checkAll("Hash[Either[Int, String]]", HashTests[Either[Int, String]].hash)
   checkAll("Hash[Map[Int, String]]", HashTests[Map[Int, String]].hash)
+  checkAll("Hash[SortedMap[Int, String]]", HashTests[SortedMap[Int, String]].hash)
   checkAll("Hash[Queue[Int]", HashTests[Queue[Int]].hash)
 
   {
diff --git a/kernel/src/main/scala-2.12-/cats/kernel/instances/AllInstances.scala b/kernel/src/main/scala-2.12-/cats/kernel/instances/AllInstances.scala
index bcbfe3addd..92cae9dd78 100644
--- a/kernel/src/main/scala-2.12-/cats/kernel/instances/AllInstances.scala
+++ b/kernel/src/main/scala-2.12-/cats/kernel/instances/AllInstances.scala
@@ -34,3 +34,5 @@ trait AllInstances
     with VectorInstances
 
 private[instances] trait AllInstancesBinCompat0 extends FiniteDurationInstances
+
+private[instances] trait AllInstancesBinCompat1 extends SortedMapInstances with SortedSetInstances
diff --git a/kernel/src/main/scala-2.13+/cats/kernel/instances/AllInstances.scala b/kernel/src/main/scala-2.13+/cats/kernel/instances/AllInstances.scala
index 66bd5d7b27..90407bb0f6 100644
--- a/kernel/src/main/scala-2.13+/cats/kernel/instances/AllInstances.scala
+++ b/kernel/src/main/scala-2.13+/cats/kernel/instances/AllInstances.scala
@@ -35,3 +35,5 @@ trait AllInstances
     with VectorInstances
 
 private[instances] trait AllInstancesBinCompat0 extends FiniteDurationInstances
+
+private[instances] trait AllInstancesBinCompat1 extends SortedMapInstances with SortedSetInstances
diff --git a/kernel/src/main/scala/cats/kernel/instances/SortedMapInstances.scala b/kernel/src/main/scala/cats/kernel/instances/SortedMapInstances.scala
new file mode 100644
index 0000000000..337fe59a45
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/SortedMapInstances.scala
@@ -0,0 +1,84 @@
+package cats.kernel
+package instances
+
+import scala.collection.immutable.SortedMap
+
+trait SortedMapInstances extends SortedMapInstances2 {
+  implicit def catsKernelStdHashForSortedMap[K: Hash: Order, V: Hash]: Hash[SortedMap[K, V]] =
+    new SortedMapHash[K, V]
+
+  implicit def catsKernelStdCommutativeMonoidForSortedMap[K: Order, V: CommutativeSemigroup]
+    : CommutativeMonoid[SortedMap[K, V]] =
+    new SortedMapCommutativeMonoid[K, V]
+}
+
+private[instances] trait SortedMapInstances1 {
+  implicit def catsKernelStdEqForSortedMap[K: Order, V: Eq]: Eq[SortedMap[K, V]] =
+    new SortedMapEq[K, V]
+}
+
+private[instances] trait SortedMapInstances2 extends SortedMapInstances1 {
+  implicit def catsKernelStdMonoidForSortedMap[K: Order, V: Semigroup]: Monoid[SortedMap[K, V]] =
+    new SortedMapMonoid[K, V]
+}
+
+class SortedMapHash[K, V](implicit V: Hash[V], O: Order[K], K: Hash[K])
+    extends SortedMapEq[K, V]()(V, O)
+    with Hash[SortedMap[K, V]] {
+  // adapted from [[scala.util.hashing.MurmurHash3]],
+  // but modified standard `Any#hashCode` to `ev.hash`.
+  import scala.util.hashing.MurmurHash3._
+  def hash(x: SortedMap[K, V]): Int = {
+    var a, b, n = 0
+    var c = 1
+    x.foreach {
+      case (k, v) =>
+        val h = StaticMethods.product2HashWithPrefix(K.hash(k), V.hash(v), "Tuple2")
+        a += h
+        b ^= h
+        c = StaticMethods.updateUnorderedHashC(c, h)
+        n += 1
+    }
+    var h = mapSeed
+    h = mix(h, a)
+    h = mix(h, b)
+    h = mixLast(h, c)
+    finalizeHash(h, n)
+  }
+}
+
+class SortedMapEq[K, V](implicit V: Eq[V], O: Order[K]) extends Eq[SortedMap[K, V]] {
+  def eqv(x: SortedMap[K, V], y: SortedMap[K, V]): Boolean =
+    if (x eq y) true
+    else
+      x.size == y.size && x.forall {
+        case (k, v1) =>
+          y.get(k) match {
+            case Some(v2) => V.eqv(v1, v2)
+            case None     => false
+          }
+      }
+}
+
+class SortedMapCommutativeMonoid[K, V](implicit V: CommutativeSemigroup[V], O: Order[K])
+    extends SortedMapMonoid[K, V]
+    with CommutativeMonoid[SortedMap[K, V]]
+
+class SortedMapMonoid[K, V](implicit V: Semigroup[V], O: Order[K]) extends Monoid[SortedMap[K, V]] {
+
+  def empty: SortedMap[K, V] = SortedMap.empty(O.toOrdering)
+
+  def combine(xs: SortedMap[K, V], ys: SortedMap[K, V]): SortedMap[K, V] =
+    if (xs.size <= ys.size) {
+      xs.foldLeft(ys) {
+        case (my, (k, x)) =>
+          my.updated(k, Semigroup.maybeCombine(x, my.get(k)))
+      }
+    } else {
+      ys.foldLeft(xs) {
+        case (mx, (k, y)) =>
+          mx.updated(k, Semigroup.maybeCombine(mx.get(k), y))
+      }
+    }
+
+}
diff --git a/kernel/src/main/scala/cats/kernel/instances/SortedSetInstances.scala b/kernel/src/main/scala/cats/kernel/instances/SortedSetInstances.scala
new file mode 100644
index 0000000000..618c6610d1
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/SortedSetInstances.scala
@@ -0,0 +1,59 @@
+package cats.kernel
+package instances
+
+import cats.kernel.{BoundedSemilattice, Hash, Order}
+import scala.collection.immutable.SortedSet
+
+trait SortedSetInstances extends SortedSetInstances1 {
+  implicit def catsKernelStdHashForSortedSet[A: Order: Hash]: Hash[SortedSet[A]] =
+    new SortedSetHash[A]
+}
+
+private[instances] trait SortedSetInstances1 {
+  implicit def catsKernelStdOrderForSortedSet[A: Order]: Order[SortedSet[A]] =
+    new SortedSetOrder[A]
+
+  implicit def catsKernelStdBoundedSemilatticeForSortedSet[A: Order]: BoundedSemilattice[SortedSet[A]] =
+    new SortedSetSemilattice[A]
+}
+
+class SortedSetOrder[A: Order] extends Order[SortedSet[A]] {
+  def compare(a1: SortedSet[A], a2: SortedSet[A]): Int =
+    cats.kernel.instances.int.catsKernelStdOrderForInt.compare(a1.size, a2.size) match {
+      case 0 => StaticMethods.iteratorCompare(a1.iterator, a2.iterator)
+      case x => x
+    }
+
+  override def eqv(s1: SortedSet[A], s2: SortedSet[A]): Boolean =
+    StaticMethods.iteratorEq(s1.iterator, s2.iterator)
+}
+
+class SortedSetHash[A: Order: Hash] extends Hash[SortedSet[A]] {
+  import scala.util.hashing.MurmurHash3._
+
+  // adapted from [[scala.util.hashing.MurmurHash3]],
+  // but modified standard `Any#hashCode` to `ev.hash`.
+  def hash(xs: SortedSet[A]): Int = {
+    var a, b, n = 0
+    var c = 1
+    xs.foreach { x =>
+      val h = Hash[A].hash(x)
+      a += h
+      b ^= h
+      c = cats.kernel.instances.StaticMethods.updateUnorderedHashC(c, h)
+      n += 1
+    }
+    var h = setSeed
+    h = mix(h, a)
+    h = mix(h, b)
+    h = mixLast(h, c)
+    finalizeHash(h, n)
+  }
+  override def eqv(s1: SortedSet[A], s2: SortedSet[A]): Boolean =
+    StaticMethods.iteratorEq(s1.iterator, s2.iterator)(Order[A])
+}
+
+class SortedSetSemilattice[A: Order] extends BoundedSemilattice[SortedSet[A]] {
+  def empty: SortedSet[A] = SortedSet.empty(implicitly[Order[A]].toOrdering)
+  def combine(x: SortedSet[A], y: SortedSet[A]): SortedSet[A] = x | y
+}
diff --git a/kernel/src/main/scala/cats/kernel/instances/all/package.scala b/kernel/src/main/scala/cats/kernel/instances/all/package.scala
index f6caf91d77..510c2b320f 100644
--- a/kernel/src/main/scala/cats/kernel/instances/all/package.scala
+++ b/kernel/src/main/scala/cats/kernel/instances/all/package.scala
@@ -1,4 +1,4 @@
 package cats.kernel
 package instances
 
-package object all extends AllInstances with AllInstancesBinCompat0
+package object all extends AllInstances with AllInstancesBinCompat0 with AllInstancesBinCompat1
diff --git a/kernel/src/main/scala/cats/kernel/instances/sortedMap/package.scala b/kernel/src/main/scala/cats/kernel/instances/sortedMap/package.scala
new file mode 100644
index 0000000000..737eef88db
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/sortedMap/package.scala
@@ -0,0 +1,4 @@
+package cats.kernel
+package instances
+
+package object sortedMap extends SortedMapInstances
diff --git a/kernel/src/main/scala/cats/kernel/instances/sortedSet/package.scala b/kernel/src/main/scala/cats/kernel/instances/sortedSet/package.scala
new file mode 100644
index 0000000000..edddfb1011
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/sortedSet/package.scala
@@ -0,0 +1,4 @@
+package cats.kernel
+package instances
+
+package object sortedSet extends SortedSetInstances
diff --git a/tests/src/test/scala/cats/tests/CatsSuite.scala b/tests/src/test/scala/cats/tests/CatsSuite.scala
index d9b2f67db7..d98191ba7f 100644
--- a/tests/src/test/scala/cats/tests/CatsSuite.scala
+++ b/tests/src/test/scala/cats/tests/CatsSuite.scala
@@ -44,6 +44,7 @@ trait CatsSuite
     with AllInstancesBinCompat3
     with AllInstancesBinCompat4
     with AllInstancesBinCompat5
+    with AllInstancesBinCompat6
     with AllSyntax
     with AllSyntaxBinCompat0
     with AllSyntaxBinCompat1