diff --git a/core/src/main/scala/cats/data/StateT.scala b/core/src/main/scala/cats/data/StateT.scala
index 7eafa57f72..61b643cba4 100644
--- a/core/src/main/scala/cats/data/StateT.scala
+++ b/core/src/main/scala/cats/data/StateT.scala
@@ -30,27 +30,6 @@ final class StateT[F[_], S, A](val runF: F[S => F[(S, A)]]) extends Serializable
   def map[B](f: A => B)(implicit F: Functor[F]): StateT[F, S, B] =
     transform { case (s, a) => (s, f(a)) }
 
-  def map2[B, Z](sb: StateT[F, S, B])(fn: (A, B) => Z)(implicit F: FlatMap[F]): StateT[F, S, Z] =
-    StateT.applyF(F.map2(runF, sb.runF) { (ssa, ssb) =>
-      ssa.andThen { fsa =>
-        F.flatMap(fsa) { case (s, a) =>
-          F.map(ssb(s)) { case (s, b) => (s, fn(a, b)) }
-        }
-      }
-    })
-
-  def map2Eval[B, Z](sb: Eval[StateT[F, S, B]])(fn: (A, B) => Z)(implicit F: FlatMap[F]): Eval[StateT[F, S, Z]] =
-    F.map2Eval(runF, sb.map(_.runF)) { (ssa, ssb) =>
-      ssa.andThen { fsa =>
-        F.flatMap(fsa) { case (s, a) =>
-          F.map(ssb(s)) { case (s, b) => (s, fn(a, b)) }
-        }
-      }
-    }.map(StateT.applyF)
-
-  def product[B](sb: StateT[F, S, B])(implicit F: FlatMap[F]): StateT[F, S, (A, B)] =
-    map2(sb)((_, _))
-
   /**
    * Run with the provided initial state value
    */
@@ -263,20 +242,8 @@ private[data] sealed trait StateTMonad[F[_], S] extends Monad[StateT[F, S, ?]] {
   def flatMap[A, B](fa: StateT[F, S, A])(f: A => StateT[F, S, B]): StateT[F, S, B] =
     fa.flatMap(f)
 
-  override def ap[A, B](ff: StateT[F, S, A => B])(fa: StateT[F, S, A]): StateT[F, S, B] =
-    ff.map2(fa) { case (f, a) => f(a) }
-
   override def map[A, B](fa: StateT[F, S, A])(f: A => B): StateT[F, S, B] = fa.map(f)
 
-  override def map2[A, B, Z](fa: StateT[F, S, A], fb: StateT[F, S, B])(fn: (A, B) => Z): StateT[F, S, Z] =
-    fa.map2(fb)(fn)
-
-  override def map2Eval[A, B, Z](fa: StateT[F, S, A], fb: Eval[StateT[F, S, B]])(fn: (A, B) => Z): Eval[StateT[F, S, Z]] =
-    fa.map2Eval(fb)(fn)
-
-  override def product[A, B](fa: StateT[F, S, A], fb: StateT[F, S, B]): StateT[F, S, (A, B)] =
-    fa.product(fb)
-
   def tailRecM[A, B](a: A)(f: A => StateT[F, S, Either[A, B]]): StateT[F, S, B] =
     StateT[F, S, B](s => F.tailRecM[(S, A), (S, B)]((s, a)) {
       case (s, a) => F.map(f(a).run(s)) { case (s, ab) => ab.bimap((s, _), (s, _)) }
diff --git a/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala b/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
index d67b4c0b02..1d80831511 100644
--- a/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
+++ b/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
@@ -167,8 +167,8 @@ object arbitrary extends ArbitraryInstances0 {
 
 private[discipline] sealed trait ArbitraryInstances0 {
 
-  implicit def catsLawArbitraryForStateT[F[_]: Applicative, S, A](implicit AS: Arbitrary[S], CS: Cogen[S], F: Arbitrary[F[(S, A)]]): Arbitrary[StateT[F, S, A]] =
-    Arbitrary(Arbitrary.arbitrary[S => F[(S, A)]].map(StateT(_)))
+  implicit def catsLawArbitraryForStateT[F[_], S, A](implicit F: Arbitrary[F[S => F[(S, A)]]]): Arbitrary[StateT[F, S, A]] =
+    Arbitrary(F.arbitrary.map(StateT.applyF))
 
   implicit def catsLawsArbitraryForWriterT[F[_], L, V](implicit F: Arbitrary[F[(L, V)]]): Arbitrary[WriterT[F, L, V]] =
     Arbitrary(F.arbitrary.map(WriterT(_)))