diff --git a/core/src/main/scala-2.13+/cats/data/NonEmptyLazyList.scala b/core/src/main/scala-2.13+/cats/data/NonEmptyLazyList.scala
index d7a9b8d14d..606b1311cd 100644
--- a/core/src/main/scala-2.13+/cats/data/NonEmptyLazyList.scala
+++ b/core/src/main/scala-2.13+/cats/data/NonEmptyLazyList.scala
@@ -473,16 +473,14 @@ sealed abstract private[data] class NonEmptyLazyListInstances extends NonEmptyLa
 
       def extract[A](fa: NonEmptyLazyList[A]): A = fa.head
 
-      def nonEmptyTraverse[G[_]: Apply, A, B](fa: NonEmptyLazyList[A])(f: A => G[B]): G[NonEmptyLazyList[B]] =
-        Foldable[LazyList]
-          .reduceRightToOption[A, G[LazyList[B]]](fa.tail)(a => Apply[G].map(f(a))(LazyList.apply(_))) { (a, lglb) =>
-            Apply[G].map2Eval(f(a), lglb)(_ +: _)
+      def nonEmptyTraverse[G[_]: Apply, A, B](fa: NonEmptyLazyList[A])(f: A => G[B]): G[NonEmptyLazyList[B]] = {
+        def loop(head: A, tail: LazyList[A]): Eval[G[NonEmptyLazyList[B]]] =
+          tail.headOption.fold(Eval.now(Apply[G].map(f(head))(NonEmptyLazyList(_)))) { h =>
+            Apply[G].map2Eval(f(head), Eval.defer(loop(h, tail.tail)))((b, acc) => b +: acc)
           }
-          .map {
-            case None        => Apply[G].map(f(fa.head))(h => create(LazyList(h)))
-            case Some(gtail) => Apply[G].map2(f(fa.head), gtail)((h, t) => create(LazyList(h) ++ t))
-          }
-          .value
+
+        loop(fa.head, fa.tail).value
+      }
 
       def reduceLeftTo[A, B](fa: NonEmptyLazyList[A])(f: A => B)(g: (B, A) => B): B = fa.reduceLeftTo(f)(g)
 
diff --git a/core/src/main/scala/cats/data/NonEmptyChain.scala b/core/src/main/scala/cats/data/NonEmptyChain.scala
index c78c9310ea..d0f577fa71 100644
--- a/core/src/main/scala/cats/data/NonEmptyChain.scala
+++ b/core/src/main/scala/cats/data/NonEmptyChain.scala
@@ -420,16 +420,14 @@ sealed abstract private[data] class NonEmptyChainInstances extends NonEmptyChain
     new AbstractNonEmptyInstances[Chain, NonEmptyChain] with Align[NonEmptyChain] {
       def extract[A](fa: NonEmptyChain[A]): A = fa.head
 
-      def nonEmptyTraverse[G[_]: Apply, A, B](fa: NonEmptyChain[A])(f: A => G[B]): G[NonEmptyChain[B]] =
-        Foldable[Chain]
-          .reduceRightToOption[A, G[Chain[B]]](fa.tail)(a => Apply[G].map(f(a))(Chain.one)) { (a, lglb) =>
-            Apply[G].map2Eval(f(a), lglb)(_ +: _)
+      def nonEmptyTraverse[G[_]: Apply, A, B](fa: NonEmptyChain[A])(f: A => G[B]): G[NonEmptyChain[B]] = {
+        def loop(head: A, tail: Chain[A]): Eval[G[NonEmptyChain[B]]] =
+          tail.uncons.fold(Eval.now(Apply[G].map(f(head))(NonEmptyChain(_)))) {
+            case (h, t) => Apply[G].map2Eval(f(head), Eval.defer(loop(h, t)))((b, acc) => b +: acc)
           }
-          .map {
-            case None        => Apply[G].map(f(fa.head))(NonEmptyChain.one)
-            case Some(gtail) => Apply[G].map2(f(fa.head), gtail)((h, t) => create(Chain.one(h) ++ t))
-          }
-          .value
+
+        loop(fa.head, fa.tail).value
+      }
 
       override def size[A](fa: NonEmptyChain[A]): Long = fa.length
 
diff --git a/core/src/main/scala/cats/data/NonEmptyList.scala b/core/src/main/scala/cats/data/NonEmptyList.scala
index 6ffd727fde..be0e1e53b2 100644
--- a/core/src/main/scala/cats/data/NonEmptyList.scala
+++ b/core/src/main/scala/cats/data/NonEmptyList.scala
@@ -562,16 +562,15 @@ sealed abstract private[data] class NonEmptyListInstances extends NonEmptyListIn
 
       def extract[A](fa: NonEmptyList[A]): A = fa.head
 
-      def nonEmptyTraverse[G[_], A, B](nel: NonEmptyList[A])(f: A => G[B])(implicit G: Apply[G]): G[NonEmptyList[B]] =
-        Foldable[List]
-          .reduceRightToOption[A, G[List[B]]](nel.tail)(a => G.map(f(a))(_ :: Nil)) { (a, lglb) =>
-            G.map2Eval(f(a), lglb)(_ :: _)
+      def nonEmptyTraverse[G[_], A, B](nel: NonEmptyList[A])(f: A => G[B])(implicit G: Apply[G]): G[NonEmptyList[B]] = {
+        def loop(head: A, tail: List[A]): Eval[G[NonEmptyList[B]]] =
+          tail match {
+            case Nil    => Eval.now(G.map(f(head))(NonEmptyList(_, Nil)))
+            case h :: t => G.map2Eval(f(head), Eval.defer(loop(h, t)))((b, acc) => NonEmptyList(b, acc.toList))
           }
-          .map {
-            case None        => G.map(f(nel.head))(NonEmptyList(_, Nil))
-            case Some(gtail) => G.map2(f(nel.head), gtail)(NonEmptyList(_, _))
-          }
-          .value
+
+        loop(nel.head, nel.tail).value
+      }
 
       override def traverse[G[_], A, B](
         fa: NonEmptyList[A]
diff --git a/core/src/main/scala/cats/data/NonEmptyMapImpl.scala b/core/src/main/scala/cats/data/NonEmptyMapImpl.scala
index 5f9a34ca88..751ecd1859 100644
--- a/core/src/main/scala/cats/data/NonEmptyMapImpl.scala
+++ b/core/src/main/scala/cats/data/NonEmptyMapImpl.scala
@@ -205,16 +205,15 @@ sealed class NonEmptyMapOps[K, A](val value: NonEmptyMap[K, A]) {
    * through the running of this function on all the values in this map,
    * returning an NonEmptyMap[K, B] in a G context.
    */
-  def nonEmptyTraverse[G[_], B](f: A => G[B])(implicit G: Apply[G]): G[NonEmptyMap[K, B]] =
-    reduceRightToOptionWithKey[A, G[SortedMap[K, B]]](tail)({
-      case (k, a) =>
-        G.map(f(a))(b => SortedMap.empty[K, B] + ((k, b)))
-    }) { (t, lglb) =>
-      G.map2Eval(f(t._2), lglb)((b, bs) => bs + ((t._1, b)))
-    }.map {
-      case None        => G.map(f(head._2))(a => NonEmptyMapImpl.one(head._1, a))
-      case Some(gtail) => G.map2(f(head._2), gtail)((a, bs) => NonEmptyMapImpl((head._1, a), bs))
-    }.value
+  def nonEmptyTraverse[G[_], B](f: A => G[B])(implicit G: Apply[G]): G[NonEmptyMap[K, B]] = {
+    def loop(h: (K, A), t: SortedMap[K, A]): Eval[G[NonEmptyMap[K, B]]] =
+      if (t.isEmpty)
+        Eval.now(G.map(f(h._2))(b => NonEmptyMap(h._1 -> b, SortedMap.empty[K, B])))
+      else
+        G.map2Eval(f(h._2), Eval.defer(loop(t.head, t.tail)))((b, acc) => NonEmptyMap(h._1 -> b, acc.toSortedMap))
+
+    loop(head, tail).value
+  }
 
   /**
    * Typesafe stringification method.
diff --git a/core/src/main/scala/cats/data/NonEmptyVector.scala b/core/src/main/scala/cats/data/NonEmptyVector.scala
index b4086cc8e1..7d29f0448c 100644
--- a/core/src/main/scala/cats/data/NonEmptyVector.scala
+++ b/core/src/main/scala/cats/data/NonEmptyVector.scala
@@ -371,17 +371,15 @@ sealed abstract private[data] class NonEmptyVectorInstances {
       def extract[A](fa: NonEmptyVector[A]): A = fa.head
 
       def nonEmptyTraverse[G[_], A, B](
-        nel: NonEmptyVector[A]
-      )(f: A => G[B])(implicit G: Apply[G]): G[NonEmptyVector[B]] =
-        Foldable[Vector]
-          .reduceRightToOption[A, G[Vector[B]]](nel.tail)(a => G.map(f(a))(_ +: Vector.empty)) { (a, lglb) =>
-            G.map2Eval(f(a), lglb)(_ +: _)
-          }
-          .map {
-            case None        => G.map(f(nel.head))(NonEmptyVector(_, Vector.empty))
-            case Some(gtail) => G.map2(f(nel.head), gtail)(NonEmptyVector(_, _))
-          }
-          .value
+        nev: NonEmptyVector[A]
+      )(f: A => G[B])(implicit G: Apply[G]): G[NonEmptyVector[B]] = {
+        def loop(head: A, tail: Vector[A]): Eval[G[NonEmptyVector[B]]] =
+          tail.headOption.fold(Eval.now(G.map(f(head))(NonEmptyVector(_, Vector.empty[B]))))(h =>
+            G.map2Eval(f(head), Eval.defer(loop(h, tail.tail)))((b, acc) => b +: acc)
+          )
+
+        loop(nev.head, nev.tail).value
+      }
 
       override def traverse[G[_], A, B](
         fa: NonEmptyVector[A]
diff --git a/core/src/main/scala/cats/data/OneAnd.scala b/core/src/main/scala/cats/data/OneAnd.scala
index a294e5a117..e6f0762b43 100644
--- a/core/src/main/scala/cats/data/OneAnd.scala
+++ b/core/src/main/scala/cats/data/OneAnd.scala
@@ -262,9 +262,20 @@ sealed abstract private[data] class OneAndLowPriority0 extends OneAndLowPriority
     F2: Alternative[F]
   ): NonEmptyTraverse[OneAnd[F, *]] =
     new NonEmptyReducible[OneAnd[F, *], F] with NonEmptyTraverse[OneAnd[F, *]] {
-      def nonEmptyTraverse[G[_], A, B](fa: OneAnd[F, A])(f: (A) => G[B])(implicit G: Apply[G]): G[OneAnd[F, B]] =
-        fa.map(a => Apply[G].map(f(a))(OneAnd(_, F2.empty[B])))(F)
-          .reduceLeft(((acc, a) => G.map2(acc, a)((x: OneAnd[F, B], y: OneAnd[F, B]) => x.combine(y))))
+      def nonEmptyTraverse[G[_], A, B](fa: OneAnd[F, A])(f: (A) => G[B])(implicit G: Apply[G]): G[OneAnd[F, B]] = {
+        import syntax.foldable._
+
+        def loop(head: A, tail: Iterator[A]): Eval[G[OneAnd[F, B]]] =
+          if (tail.hasNext) {
+            val h = tail.next()
+            val t = tail
+            G.map2Eval(f(head), Eval.defer(loop(h, t)))((b, acc) => OneAnd(b, acc.unwrap))
+          } else {
+            Eval.now(G.map(f(head))(OneAnd(_, F2.empty[B])))
+          }
+
+        loop(fa.head, fa.tail.toIterable.iterator).value
+      }
 
       override def traverse[G[_], A, B](fa: OneAnd[F, A])(f: (A) => G[B])(implicit G: Applicative[G]): G[OneAnd[F, B]] =
         G.map2Eval(f(fa.head), Always(F.traverse(fa.tail)(f)))(OneAnd(_, _)).value
diff --git a/laws/src/main/scala/cats/laws/ShortCircuitingLaws.scala b/laws/src/main/scala/cats/laws/ShortCircuitingLaws.scala
index 6d4300cc55..ca8e0c4d22 100644
--- a/laws/src/main/scala/cats/laws/ShortCircuitingLaws.scala
+++ b/laws/src/main/scala/cats/laws/ShortCircuitingLaws.scala
@@ -5,8 +5,9 @@ import java.util.concurrent.atomic.AtomicLong
 import cats.instances.option._
 import cats.syntax.foldable._
 import cats.syntax.traverse._
+import cats.syntax.nonEmptyTraverse._
 import cats.syntax.traverseFilter._
-import cats.{Applicative, Foldable, MonoidK, Traverse, TraverseFilter}
+import cats.{Applicative, Foldable, MonoidK, NonEmptyTraverse, Traverse, TraverseFilter}
 
 trait ShortCircuitingLaws[F[_]] {
 
@@ -46,6 +47,24 @@ trait ShortCircuitingLaws[F[_]] {
     f.invocations.get <-> size
   }
 
+  def nonEmptyTraverseShortCircuits[A](fa: F[A])(implicit F: NonEmptyTraverse[F]): IsEq[Long] = {
+    val size = fa.size
+    val maxInvocationsAllowed = size / 2
+    val f = new RestrictedFunction((i: A) => Some(i), maxInvocationsAllowed, None)
+
+    fa.nonEmptyTraverse(f)
+    f.invocations.get <-> (maxInvocationsAllowed + 1).min(size)
+  }
+
+  def nonEmptyTraverseWontShortCircuit[A](fa: F[A])(implicit F: NonEmptyTraverse[F]): IsEq[Long] = {
+    val size = fa.size
+    val maxInvocationsAllowed = size / 2
+    val f = new RestrictedFunction((i: A) => Some(i), maxInvocationsAllowed, None)
+
+    fa.nonEmptyTraverse(f)(nonShortCircuitingApplicative)
+    f.invocations.get <-> size
+  }
+
   def traverseFilterShortCircuits[A](fa: F[A])(implicit TF: TraverseFilter[F]): IsEq[Long] = {
     implicit val F: Traverse[F] = TF.traverse
 
diff --git a/laws/src/main/scala/cats/laws/discipline/ShortCircuitingTests.scala b/laws/src/main/scala/cats/laws/discipline/ShortCircuitingTests.scala
index 1f40605a13..91234710ea 100644
--- a/laws/src/main/scala/cats/laws/discipline/ShortCircuitingTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/ShortCircuitingTests.scala
@@ -1,7 +1,7 @@
 package cats.laws.discipline
 
 import cats.laws.ShortCircuitingLaws
-import cats.{Eq, Foldable, Traverse, TraverseFilter}
+import cats.{Eq, Foldable, NonEmptyTraverse, Traverse, TraverseFilter}
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop.forAll
 import org.typelevel.discipline.Laws
@@ -25,11 +25,17 @@ trait ShortCircuitingTests[F[_]] extends Laws {
       "traverse won't short-circuit if Applicative[G].map2Eval won't" -> forAll(laws.traverseWontShortCircuit[A] _)
     )
 
-  def traverseFilter[A: Arbitrary](implicit
-    TF: TraverseFilter[F],
-    ArbFA: Arbitrary[F[A]],
-    lEq: Eq[Long]
-  ): RuleSet = {
+  def nonEmptyTraverse[A: Arbitrary](implicit TF: NonEmptyTraverse[F], ArbFA: Arbitrary[F[A]], lEq: Eq[Long]): RuleSet =
+    new DefaultRuleSet(
+      name = "nonEmptyTraverseShortCircuiting",
+      parent = Some(traverse[A]),
+      "nonEmptyTraverse short-circuits if Applicative[G].map2Eval shorts" ->
+        forAll(laws.nonEmptyTraverseShortCircuits[A] _),
+      "nonEmptyTraverse short-circuits if Applicative[G].map2Eval won't" ->
+        forAll(laws.nonEmptyTraverseWontShortCircuit[A] _)
+    )
+
+  def traverseFilter[A: Arbitrary](implicit TF: TraverseFilter[F], ArbFA: Arbitrary[F[A]], lEq: Eq[Long]): RuleSet = {
     implicit val T: Traverse[F] = TF.traverse
     new DefaultRuleSet(
       name = "traverseFilterShortCircuiting",
diff --git a/tests/src/test/scala-2.12/cats/tests/NonEmptyStreamSuite.scala b/tests/src/test/scala-2.12/cats/tests/NonEmptyStreamSuite.scala
index 7ab74d33ec..45f804abbf 100644
--- a/tests/src/test/scala-2.12/cats/tests/NonEmptyStreamSuite.scala
+++ b/tests/src/test/scala-2.12/cats/tests/NonEmptyStreamSuite.scala
@@ -32,6 +32,7 @@ class NonEmptyStreamSuite extends CatsSuite {
 
   checkAll("NonEmptyStream[Int]", ShortCircuitingTests[NonEmptyStream].foldable[Int])
   checkAll("NonEmptyStream[Int]", ShortCircuitingTests[NonEmptyStream].traverse[Int])
+  checkAll("NonEmptyStream[Int]", ShortCircuitingTests[NonEmptyStream].nonEmptyTraverse[Int])
 
   {
     // Test functor and subclasses don't have implicit conflicts
diff --git a/tests/src/test/scala-2.13+/cats/tests/NonEmptyLazyListSuite.scala b/tests/src/test/scala-2.13+/cats/tests/NonEmptyLazyListSuite.scala
index 794a15f316..9260311c1e 100644
--- a/tests/src/test/scala-2.13+/cats/tests/NonEmptyLazyListSuite.scala
+++ b/tests/src/test/scala-2.13+/cats/tests/NonEmptyLazyListSuite.scala
@@ -46,6 +46,7 @@ class NonEmptyLazyListSuite extends NonEmptyCollectionSuite[LazyList, NonEmptyLa
 
   checkAll("NonEmptyLazyList[Int]", ShortCircuitingTests[NonEmptyLazyList].foldable[Int])
   checkAll("NonEmptyLazyList[Int]", ShortCircuitingTests[NonEmptyLazyList].traverse[Int])
+  checkAll("NonEmptyLazyList[Int]", ShortCircuitingTests[NonEmptyLazyList].nonEmptyTraverse[Int])
 
   test("show") {
     Show[NonEmptyLazyList[Int]].show(NonEmptyLazyList(1, 2, 3)) should ===("NonEmptyLazyList(1, ?)")
diff --git a/tests/src/test/scala/cats/tests/NonEmptyChainSuite.scala b/tests/src/test/scala/cats/tests/NonEmptyChainSuite.scala
index 9b7670a58d..2d6566ef85 100644
--- a/tests/src/test/scala/cats/tests/NonEmptyChainSuite.scala
+++ b/tests/src/test/scala/cats/tests/NonEmptyChainSuite.scala
@@ -43,6 +43,7 @@ class NonEmptyChainSuite extends NonEmptyCollectionSuite[Chain, NonEmptyChain, N
 
   checkAll("NonEmptyChain[Int]", ShortCircuitingTests[NonEmptyChain].foldable[Int])
   checkAll("NonEmptyChain[Int]", ShortCircuitingTests[NonEmptyChain].traverse[Int])
+  checkAll("NonEmptyChain[Int]", ShortCircuitingTests[NonEmptyChain].nonEmptyTraverse[Int])
 
   {
     implicit val partialOrder: PartialOrder[ListWrapper[Int]] = ListWrapper.partialOrder[Int]
diff --git a/tests/src/test/scala/cats/tests/NonEmptyListSuite.scala b/tests/src/test/scala/cats/tests/NonEmptyListSuite.scala
index fb2a906ac2..13b9412be6 100644
--- a/tests/src/test/scala/cats/tests/NonEmptyListSuite.scala
+++ b/tests/src/test/scala/cats/tests/NonEmptyListSuite.scala
@@ -59,6 +59,7 @@ class NonEmptyListSuite extends NonEmptyCollectionSuite[List, NonEmptyList, NonE
 
   checkAll("NonEmptyList[Int]", ShortCircuitingTests[NonEmptyList].foldable[Int])
   checkAll("NonEmptyList[Int]", ShortCircuitingTests[NonEmptyList].traverse[Int])
+  checkAll("NonEmptyList[Int]", ShortCircuitingTests[NonEmptyList].nonEmptyTraverse[Int])
 
   {
     implicit val A: PartialOrder[ListWrapper[Int]] = ListWrapper.partialOrder[Int]
diff --git a/tests/src/test/scala/cats/tests/NonEmptyMapSuite.scala b/tests/src/test/scala/cats/tests/NonEmptyMapSuite.scala
index bbdb89e73c..06454c9eed 100644
--- a/tests/src/test/scala/cats/tests/NonEmptyMapSuite.scala
+++ b/tests/src/test/scala/cats/tests/NonEmptyMapSuite.scala
@@ -25,6 +25,8 @@ class NonEmptyMapSuite extends CatsSuite {
   checkAll("NonEmptyMap[String, Int]", AlignTests[NonEmptyMap[String, *]].align[Int, Int, Int, Int])
   checkAll("Align[NonEmptyMap]", SerializableTests.serializable(Align[NonEmptyMap[String, *]]))
 
+  checkAll("NonEmptyMap[Int, *]", ShortCircuitingTests[NonEmptyMap[Int, *]].nonEmptyTraverse[Int])
+
   test("Show is not empty and is formatted as expected") {
     forAll { (nem: NonEmptyMap[String, Int]) =>
       nem.show.nonEmpty should ===(true)
diff --git a/tests/src/test/scala/cats/tests/NonEmptyVectorSuite.scala b/tests/src/test/scala/cats/tests/NonEmptyVectorSuite.scala
index 30df9d5363..048731e1d4 100644
--- a/tests/src/test/scala/cats/tests/NonEmptyVectorSuite.scala
+++ b/tests/src/test/scala/cats/tests/NonEmptyVectorSuite.scala
@@ -86,6 +86,7 @@ class NonEmptyVectorSuite extends NonEmptyCollectionSuite[Vector, NonEmptyVector
 
   checkAll("NonEmptyVector[Int]", ShortCircuitingTests[NonEmptyVector].foldable[Int])
   checkAll("NonEmptyVector[Int]", ShortCircuitingTests[NonEmptyVector].traverse[Int])
+  checkAll("NonEmptyVector[Int]", ShortCircuitingTests[NonEmptyVector].nonEmptyTraverse[Int])
 
   test("size is consistent with toList.size") {
     forAll { (nonEmptyVector: NonEmptyVector[Int]) =>