diff --git a/core/src/main/scala/cats/data/EitherK.scala b/core/src/main/scala/cats/data/EitherK.scala
index e62fa7d509..6872e87604 100644
--- a/core/src/main/scala/cats/data/EitherK.scala
+++ b/core/src/main/scala/cats/data/EitherK.scala
@@ -140,7 +140,7 @@ private[data] sealed abstract class EitherKInstances2 extends EitherKInstances3
 
 private[data] sealed abstract class EitherKInstances1 extends EitherKInstances2 {
   implicit def catsDataCoflatMapForEitherK[F[_], G[_]](implicit F0: CoflatMap[F], G0: CoflatMap[G]): CoflatMap[EitherK[F, G, ?]] =
-    new EitherKCoflatMap[F, G] {
+    new EitherKCoflatMap[F, G] with EitherKFunctor[F, G] {
       implicit def F: CoflatMap[F] = F0
 
       implicit def G: CoflatMap[G] = G0
@@ -149,7 +149,7 @@ private[data] sealed abstract class EitherKInstances1 extends EitherKInstances2
 
 private[data] sealed abstract class EitherKInstances0 extends EitherKInstances1 {
   implicit def catsDataTraverseForEitherK[F[_], G[_]](implicit F0: Traverse[F], G0: Traverse[G]): Traverse[EitherK[F, G, ?]] =
-    new EitherKTraverse[F, G] {
+    new EitherKTraverse[F, G] with EitherKFunctor[F, G] {
       implicit def F: Traverse[F] = F0
 
       implicit def G: Traverse[G] = G0
@@ -159,7 +159,7 @@ private[data] sealed abstract class EitherKInstances0 extends EitherKInstances1
 private[data] sealed abstract class EitherKInstances extends EitherKInstances0 {
 
   implicit def catsDataComonadForEitherK[F[_], G[_]](implicit F0: Comonad[F], G0: Comonad[G]): Comonad[EitherK[F, G, ?]] =
-    new EitherKComonad[F, G] {
+    new EitherKComonad[F, G] with EitherKFunctor[F, G] {
       implicit def F: Comonad[F] = F0
 
       implicit def G: Comonad[G] = G0
@@ -171,7 +171,7 @@ private[data] trait EitherKFunctor[F[_], G[_]] extends Functor[EitherK[F, G, ?]]
 
   implicit def G: Functor[G]
 
-  def map[A, B](a: EitherK[F, G, A])(f: A => B): EitherK[F, G, B] =
+  override def map[A, B](a: EitherK[F, G, A])(f: A => B): EitherK[F, G, B] =
     a map f
 }
 
diff --git a/core/src/main/scala/cats/data/EitherT.scala b/core/src/main/scala/cats/data/EitherT.scala
index 516034d7d0..748c1b029b 100644
--- a/core/src/main/scala/cats/data/EitherT.scala
+++ b/core/src/main/scala/cats/data/EitherT.scala
@@ -469,13 +469,14 @@ private[data] abstract class EitherTInstances extends EitherTInstances1 {
     Contravariant[Show].contramap(sh)(_.value)
 
   implicit def catsDataBifunctorForEitherT[F[_]](implicit F: Functor[F]): Bifunctor[EitherT[F, ?, ?]] =
-    new Bifunctor[EitherT[F, ?, ?]] {
-      override def bimap[A, B, C, D](fab: EitherT[F, A, B])(f: A => C, g: B => D): EitherT[F, C, D] = fab.bimap(f, g)
+    new EitherTBifunctor[F] {
+      val F0: Functor[F] = F
     }
 
-  implicit def catsDataTraverseForEitherT[F[_], L](implicit F: Traverse[F]): Traverse[EitherT[F, L, ?]] =
-    new EitherTTraverse[F, L] {
-      val F0: Traverse[F] = F
+  implicit def catsDataTraverseForEitherT[F[_], L](implicit FF: Traverse[F]): Traverse[EitherT[F, L, ?]] =
+    new EitherTTraverse[F, L] with EitherTFunctor[F, L] {
+      val F0: Traverse[F] = FF
+      val F: Functor[F] = FF
     }
 
   implicit def catsMonoidForEitherT[F[_], L, A](implicit F: Monoid[F[Either[L, A]]]): Monoid[EitherT[F, L, A]] =
@@ -499,7 +500,7 @@ private[data] abstract class EitherTInstances1 extends EitherTInstances2 {
     }
 
   implicit def catsDataBitraverseForEitherT[F[_]](implicit F: Traverse[F]): Bitraverse[EitherT[F, ?, ?]] =
-    new EitherTBitraverse[F] {
+    new EitherTBitraverse[F] with EitherTBifunctor[F] {
       val F0: Traverse[F] = F
     }
 
@@ -647,6 +648,12 @@ private[data] sealed trait EitherTBitraverse[F[_]] extends Bitraverse[EitherT[F,
     fab.bitraverse(f, g)
 }
 
+private[data] sealed trait EitherTBifunctor[F[_]] extends Bifunctor[EitherT[F, ?, ?]] {
+  implicit def F0: Functor[F]
+
+  override def bimap[A, B, C, D](fab: EitherT[F, A, B])(f: A => C, g: B => D): EitherT[F, C, D] = fab.bimap(f, g)
+}
+
 private[data] sealed trait EitherTEq[F[_], L, A] extends Eq[EitherT[F, L, A]] {
   implicit def F0: Eq[F[Either[L, A]]]
 
diff --git a/core/src/main/scala/cats/data/IndexedReaderWriterStateT.scala b/core/src/main/scala/cats/data/IndexedReaderWriterStateT.scala
index 2514bc8aa6..375657a80b 100644
--- a/core/src/main/scala/cats/data/IndexedReaderWriterStateT.scala
+++ b/core/src/main/scala/cats/data/IndexedReaderWriterStateT.scala
@@ -563,7 +563,24 @@ private[data] sealed abstract class RWSTMonad[F[_], E, L, S] extends IRWSTFuncto
     }
 }
 
-private[data] sealed abstract class IRWSTSemigroupK[F[_], E, L, SA, SB] extends SemigroupK[IndexedReaderWriterStateT[F, E, L, SA, SB, ?]] {
+private[data] sealed abstract class IRWSTSemigroupK[F[_], E, L, SA, SB] extends IRWSTSemigroupK1[F, E, L, SA, SB]
+
+private[data] sealed abstract class RWSTAlternative[F[_], E, L, S] extends IRWSTFunctor[F, E, L, S, S] with RWSTAlternative1[F, E, L, S]
+
+private[data] sealed abstract class RWSTMonadError[F[_], E, L, S, R]
+    extends RWSTMonad[F, E, L, S] with MonadError[ReaderWriterStateT[F, E, L, S, ?], R] {
+
+  implicit def F: MonadError[F, R]
+
+  def raiseError[A](r: R): ReaderWriterStateT[F, E, L, S, A] = ReaderWriterStateT.liftF(F.raiseError(r))
+
+  def handleErrorWith[A](fa: ReaderWriterStateT[F, E, L, S, A])(f: R => ReaderWriterStateT[F, E, L, S, A]): ReaderWriterStateT[F, E, L, S, A] =
+    ReaderWriterStateT { (e, s) =>
+      F.handleErrorWith(fa.run(e, s))(r => f(r).run(e, s))
+    }
+}
+
+private trait IRWSTSemigroupK1[F[_], E, L, SA, SB] extends SemigroupK[IndexedReaderWriterStateT[F, E, L, SA, SB, ?]] {
   implicit def F: Monad[F]
   implicit def G: SemigroupK[F]
 
@@ -574,19 +591,12 @@ private[data] sealed abstract class IRWSTSemigroupK[F[_], E, L, SA, SB] extends
     }
 }
 
-private[data] sealed abstract class RWSTAlternative[F[_], E, L, S]
-  extends IRWSTFunctor[F, E, L, S, S] with Alternative[ReaderWriterStateT[F, E, L, S, ?]] {
+private trait RWSTAlternative1[F[_], E, L, S] extends IRWSTSemigroupK1[F, E, L, S, S] with Alternative[ReaderWriterStateT[F, E, L, S, ?]] {
 
   implicit def F: Monad[F]
   def G: Alternative[F]
   implicit def L: Monoid[L]
 
-  def combineK[A](x: ReaderWriterStateT[F, E, L, S, A],
-    y: ReaderWriterStateT[F, E, L, S, A]): ReaderWriterStateT[F, E, L, S, A] =
-    ReaderWriterStateT { (e, sa) =>
-      G.combineK(x.run(e, sa), y.run(e, sa))
-    }
-
   def empty[A]: ReaderWriterStateT[F, E, L, S, A] = ReaderWriterStateT.liftF(G.empty[A])
 
   def pure[A](a: A): ReaderWriterStateT[F, E, L, S, A] = ReaderWriterStateT.pure[F, E, L, S, A](a)
@@ -595,16 +605,3 @@ private[data] sealed abstract class RWSTAlternative[F[_], E, L, S]
     ff.flatMap(f => fa.map(f)(F))(F, L)
 
 }
-
-private[data] sealed abstract class RWSTMonadError[F[_], E, L, S, R]
-    extends RWSTMonad[F, E, L, S] with MonadError[ReaderWriterStateT[F, E, L, S, ?], R] {
-
-  implicit def F: MonadError[F, R]
-
-  def raiseError[A](r: R): ReaderWriterStateT[F, E, L, S, A] = ReaderWriterStateT.liftF(F.raiseError(r))
-
-  def handleErrorWith[A](fa: ReaderWriterStateT[F, E, L, S, A])(f: R => ReaderWriterStateT[F, E, L, S, A]): ReaderWriterStateT[F, E, L, S, A] =
-    ReaderWriterStateT { (e, s) =>
-      F.handleErrorWith(fa.run(e, s))(r => f(r).run(e, s))
-    }
-}
diff --git a/core/src/main/scala/cats/data/IorT.scala b/core/src/main/scala/cats/data/IorT.scala
index d9f4292ea1..0a73124619 100644
--- a/core/src/main/scala/cats/data/IorT.scala
+++ b/core/src/main/scala/cats/data/IorT.scala
@@ -410,7 +410,7 @@ private[data] abstract class IorTInstances extends IorTInstances1 {
     }
 
   implicit def catsDataTraverseForIorT[F[_], A](implicit F: Traverse[F]): Traverse[IorT[F, A, ?]] =
-    new IorTTraverse[F, A] { val F0: Traverse[F] = F }
+    new IorTTraverse[F, A] with IorTFunctor[F, A] { val F0: Traverse[F] = F }
 
   implicit def catsDataMonoidForIorT[F[_], A, B](implicit F: Monoid[F[Ior[A, B]]]): Monoid[IorT[F, A, B]] =
     new IorTMonoid[F, A, B] { val F0: Monoid[F[Ior[A, B]]] = F }
diff --git a/core/src/main/scala/cats/data/Kleisli.scala b/core/src/main/scala/cats/data/Kleisli.scala
index fcdb3e8d3e..c0f9f264c5 100644
--- a/core/src/main/scala/cats/data/Kleisli.scala
+++ b/core/src/main/scala/cats/data/Kleisli.scala
@@ -266,7 +266,7 @@ private[data] sealed abstract class KleisliInstances6 extends KleisliInstances7
 
 private[data] sealed abstract class KleisliInstances7 extends KleisliInstances8 {
   implicit def catsDataDistributiveForKleisli[F[_], R](implicit F0: Distributive[F]): Distributive[Kleisli[F, R, ?]] =
-    new KleisliDistributive[F, R] { implicit def F: Distributive[F] = F0 }
+    new KleisliDistributive[F, R] with KleisliFunctor[F, R] { implicit def F: Distributive[F] = F0 }
 }
 
 private[data] sealed abstract class KleisliInstances8 {
diff --git a/core/src/main/scala/cats/data/Nested.scala b/core/src/main/scala/cats/data/Nested.scala
index 2dd937e288..e37ae2f667 100644
--- a/core/src/main/scala/cats/data/Nested.scala
+++ b/core/src/main/scala/cats/data/Nested.scala
@@ -45,7 +45,7 @@ private[data] sealed abstract class NestedInstances extends NestedInstances0 {
     }
 
   implicit def catsDataContravariantMonoidalForApplicativeForNested[F[_]: Applicative, G[_]: ContravariantMonoidal]: ContravariantMonoidal[Nested[F, G, ?]] =
-    new NestedContravariantMonoidal[F, G] {
+    new NestedContravariantMonoidal[F, G] with NestedContravariant[F, G] {
       val FG: ContravariantMonoidal[λ[α => F[G[α]]]] = Applicative[F].composeContravariantMonoidal[G]
     }
 }
@@ -284,7 +284,7 @@ private[data] trait NestedNonEmptyTraverse[F[_], G[_]] extends NonEmptyTraverse[
 private[data] trait NestedContravariant[F[_], G[_]] extends Contravariant[Nested[F, G, ?]] {
   def FG: Contravariant[λ[α => F[G[α]]]]
 
-  def contramap[A, B](fga: Nested[F, G, A])(f: B => A): Nested[F, G, B] =
+  override def contramap[A, B](fga: Nested[F, G, A])(f: B => A): Nested[F, G, B] =
     Nested(FG.contramap(fga.value)(f))
 }
 
diff --git a/core/src/main/scala/cats/data/OptionT.scala b/core/src/main/scala/cats/data/OptionT.scala
index 6b587d0dce..74fb633fb5 100644
--- a/core/src/main/scala/cats/data/OptionT.scala
+++ b/core/src/main/scala/cats/data/OptionT.scala
@@ -258,7 +258,7 @@ private[data] sealed abstract class OptionTInstances1 extends OptionTInstances2
 
 private[data] sealed abstract class OptionTInstances2 extends OptionTInstances3 {
   implicit def catsDataTraverseForOptionT[F[_]](implicit F0: Traverse[F]): Traverse[OptionT[F, ?]] =
-    new OptionTTraverse[F] { implicit val F = F0 }
+    new OptionTTraverse[F] with OptionTFunctor[F] { implicit val F = F0 }
 }
 
 private[data] sealed abstract class OptionTInstances3 {
diff --git a/core/src/main/scala/cats/data/Tuple2K.scala b/core/src/main/scala/cats/data/Tuple2K.scala
index efa0242c7a..cfce28ccca 100644
--- a/core/src/main/scala/cats/data/Tuple2K.scala
+++ b/core/src/main/scala/cats/data/Tuple2K.scala
@@ -30,17 +30,18 @@ private[data] sealed abstract class Tuple2KInstances extends Tuple2KInstances0 {
     def G: Show[G[A]] = GF
   }
   implicit def catsDataContravariantMonoidalForTuple2k[F[_], G[_]](implicit FD: ContravariantMonoidal[F], GD: ContravariantMonoidal[G]): ContravariantMonoidal[λ[α => Tuple2K[F, G, α]]] =
-    new Tuple2KContravariantMonoidal[F, G] {
+    new Tuple2KContravariantMonoidal[F, G] with Tuple2KContravariant[F, G] {
       def F: ContravariantMonoidal[F] = FD
       def G: ContravariantMonoidal[G] = GD
     }
 }
 
 private[data] sealed abstract class Tuple2KInstances0 extends Tuple2KInstances1 {
-  implicit def catsDataTraverseForTuple2K[F[_], G[_]](implicit FF: Traverse[F], GF: Traverse[G]): Traverse[λ[α => Tuple2K[F, G, α]]] = new Tuple2KTraverse[F, G] {
-    def F: Traverse[F] = FF
-    def G: Traverse[G] = GF
-  }
+  implicit def catsDataTraverseForTuple2K[F[_], G[_]](implicit FF: Traverse[F], GF: Traverse[G]): Traverse[λ[α => Tuple2K[F, G, α]]] =
+    new Tuple2KTraverse[F, G] with Tuple2KFunctor[F, G] {
+      def F: Traverse[F] = FF
+      def G: Traverse[G] = GF
+    }
   implicit def catsDataContravariantForTuple2K[F[_], G[_]](implicit FC: Contravariant[F], GC: Contravariant[G]): Contravariant[λ[α => Tuple2K[F, G, α]]] = new Tuple2KContravariant[F, G] {
     def F: Contravariant[F] = FC
     def G: Contravariant[G] = GC
@@ -109,10 +110,11 @@ private[data] sealed abstract class Tuple2KInstances6 extends Tuple2KInstances7
 }
 
 private[data] sealed abstract class Tuple2KInstances7 extends Tuple2KInstances8 {
-  implicit def catsDataDistributiveForTuple2K[F[_], G[_]](implicit FF: Distributive[F], GG: Distributive[G]): Distributive[λ[α => Tuple2K[F, G, α]]] = new Tuple2KDistributive[F, G] {
-    def F: Distributive[F] = FF
-    def G: Distributive[G] = GG
-  }
+  implicit def catsDataDistributiveForTuple2K[F[_], G[_]](implicit FF: Distributive[F], GG: Distributive[G]): Distributive[λ[α => Tuple2K[F, G, α]]] =
+    new Tuple2KDistributive[F, G] with Tuple2KFunctor[F, G] {
+      def F: Distributive[F] = FF
+      def G: Distributive[G] = GG
+    }
 }
 
 private[data] sealed abstract class Tuple2KInstances8 {
@@ -132,14 +134,19 @@ private[data] sealed trait Tuple2KFunctor[F[_], G[_]] extends Functor[λ[α => T
 private[data] sealed trait Tuple2KDistributive[F[_], G[_]] extends Distributive[λ[α => Tuple2K[F, G, α]]] {
   def F: Distributive[F]
   def G: Distributive[G]
-  override def distribute[H[_]: Functor, A, B](ha: H[A])(f: A => Tuple2K[F, G, B]): Tuple2K[F, G, H[B]] = Tuple2K(F.distribute(ha){a => f(a).first}, G.distribute(ha){a => f(a).second})
-  override def map[A, B](fa: Tuple2K[F, G, A])(f: A => B): Tuple2K[F, G, B] = Tuple2K(F.map(fa.first)(f), G.map(fa.second)(f))
+
+  override def distribute[H[_]: Functor, A, B](ha: H[A])(f: A => Tuple2K[F, G, B]): Tuple2K[F, G, H[B]] =
+    Tuple2K(F.distribute(ha){a => f(a).first}, G.distribute(ha){a => f(a).second})
+
+  override def map[A, B](fa: Tuple2K[F, G, A])(f: A => B): Tuple2K[F, G, B] =
+    Tuple2K(F.map(fa.first)(f), G.map(fa.second)(f))
 }
 
 private[data] sealed trait Tuple2KContravariant[F[_], G[_]] extends Contravariant[λ[α => Tuple2K[F, G, α]]] {
   def F: Contravariant[F]
   def G: Contravariant[G]
-  def contramap[A, B](fa: Tuple2K[F, G, A])(f: B => A): Tuple2K[F, G, B] = Tuple2K(F.contramap(fa.first)(f), G.contramap(fa.second)(f))
+  override def contramap[A, B](fa: Tuple2K[F, G, A])(f: B => A): Tuple2K[F, G, B] =
+    Tuple2K(F.contramap(fa.first)(f), G.contramap(fa.second)(f))
 }
 
 private[data] sealed trait Tuple2KContravariantMonoidal[F[_], G[_]] extends ContravariantMonoidal[λ[α => Tuple2K[F, G, α]]] {
diff --git a/core/src/main/scala/cats/data/WriterT.scala b/core/src/main/scala/cats/data/WriterT.scala
index 1f09eb8723..221c572808 100644
--- a/core/src/main/scala/cats/data/WriterT.scala
+++ b/core/src/main/scala/cats/data/WriterT.scala
@@ -297,7 +297,7 @@ private[data] sealed trait WriterTFunctor[F[_], L] extends Functor[WriterT[F, L,
 private[data] sealed trait WriterTContravariant[F[_], L] extends Contravariant[WriterT[F, L, ?]] {
   implicit def F0: Contravariant[F]
 
-  def contramap[A, B](fa: WriterT[F, L, A])(f: B => A): WriterT[F, L, B] =
+  override def contramap[A, B](fa: WriterT[F, L, A])(f: B => A): WriterT[F, L, B] =
     fa.contramap(f)
 }
 
@@ -420,7 +420,7 @@ private[data] sealed trait WriterTContravariantMonoidal[F[_], L] extends Contrav
   override def unit: WriterT[F, L, Unit] = WriterT(F0.trivial[(L, Unit)])
 
   override def contramap[A, B](fa: WriterT[F, L, A])(f: B => A): WriterT[F, L, B] =
-    WriterT(F0.contramap(fa.run)((d: (L, B)) => (d._1, f(d._2))))
+    fa.contramap(f)
 
   override def product[A, B](fa: WriterT[F, L, A], fb: WriterT[F, L, B]): WriterT[F, L, (A, B)] =
     WriterT(
diff --git a/tests/src/test/scala/cats/tests/NestedSuite.scala b/tests/src/test/scala/cats/tests/NestedSuite.scala
index 3b52227594..fff27f9904 100644
--- a/tests/src/test/scala/cats/tests/NestedSuite.scala
+++ b/tests/src/test/scala/cats/tests/NestedSuite.scala
@@ -89,8 +89,10 @@ class NestedSuite extends CatsSuite {
 
   {
     // CommutativeApply composition
+    implicit val optionApply = Apply[Option]
+    implicit val validatedApply = Apply[Validated[Int, ?]]
     checkAll("Nested[Option, Validated[Int, ?], ?]", CommutativeApplyTests[Nested[Option, Validated[Int, ?], ?]].commutativeApply[Int, Int, Int])
-    checkAll("CommutativeApply[Nested[List, ListWrapper, ?]]", SerializableTests.serializable(CommutativeApply[Nested[Option, Validated[Int, ?], ?]]))
+    checkAll("CommutativeApply[Nested[Option, Validated[Int, ?], ?], ?]]", SerializableTests.serializable(CommutativeApply[Nested[Option, Validated[Int, ?], ?]]))
   }
 
   {
diff --git a/tests/src/test/scala/cats/tests/Tuple2KSuite.scala b/tests/src/test/scala/cats/tests/Tuple2KSuite.scala
index a2fc73a6a7..91802a4ff8 100644
--- a/tests/src/test/scala/cats/tests/Tuple2KSuite.scala
+++ b/tests/src/test/scala/cats/tests/Tuple2KSuite.scala
@@ -47,6 +47,8 @@ class Tuple2KSuite extends CatsSuite {
   }
 
   {
+    implicit val optionApply = Apply[Option]
+    implicit val validatedApply = Apply[Validated[Int, ?]]
     checkAll("Tuple2K[Option, Validated[Int, ?], ?]", CommutativeApplyTests[Tuple2K[Option, Validated[Int, ?], ?]].commutativeApply[Int, Int, Int])
     checkAll("Apply[Tuple2K[Option, Validated[Int, ?], ?]]", SerializableTests.serializable(CommutativeApply[Tuple2K[Option, Validated[Int, ?], ?]]))
   }
diff --git a/tests/src/test/scala/cats/tests/WriterTSuite.scala b/tests/src/test/scala/cats/tests/WriterTSuite.scala
index 19b98868ab..274afd9798 100644
--- a/tests/src/test/scala/cats/tests/WriterTSuite.scala
+++ b/tests/src/test/scala/cats/tests/WriterTSuite.scala
@@ -404,8 +404,6 @@ class WriterTSuite extends CatsSuite {
 
   {
     // F has a Comonad and L has a Monoid
-    implicit val L: Monoid[ListWrapper[Int]] = ListWrapper.monoid[Int]
-    Comonad[(String, ?)]
     Comonad[WriterT[(String, ?), ListWrapper[Int], ?]]
 
     checkAll("WriterT[(String, ?), ListWrapper[Int], ?]", ComonadTests[WriterT[(String, ?), ListWrapper[Int], ?]].comonad[Int, Int, Int])