diff --git a/core/src/main/scala/cats/data/EitherT.scala b/core/src/main/scala/cats/data/EitherT.scala
index ba59b02163..1b51488624 100644
--- a/core/src/main/scala/cats/data/EitherT.scala
+++ b/core/src/main/scala/cats/data/EitherT.scala
@@ -432,7 +432,7 @@ private[data] trait EitherTFunctor[F[_], L] extends Functor[EitherT[F, L, ?]] {
 
 private[data] trait EitherTMonad[F[_], L] extends Monad[EitherT[F, L, ?]] with EitherTFunctor[F, L] {
   implicit val F: Monad[F]
-  def pure[A](a: A): EitherT[F, L, A] = EitherT(F.pure(Either.right(a)))
+  def pure[A](a: A): EitherT[F, L, A] = EitherT.pure(a)
   def flatMap[A, B](fa: EitherT[F, L, A])(f: A => EitherT[F, L, B]): EitherT[F, L, B] = fa flatMap f
   def tailRecM[A, B](a: A)(f: A => EitherT[F, L, Either[A, B]]): EitherT[F, L, B] =
     EitherT(F.tailRecM(a)(a0 => F.map(f(a0).value) {
@@ -461,11 +461,13 @@ private[data] trait EitherTMonadError[F[_], L] extends MonadError[EitherT[F, L,
     fla.recoverWith(pf)
 }
 
+/* TODO violates monadFilter right empty law -- re-enable when MonadFilter laws are split in to weak/strong
 private[data] trait EitherTMonadFilter[F[_], L] extends MonadFilter[EitherT[F, L, ?]] with EitherTMonadError[F, L] {
   implicit val F: Monad[F]
   implicit val L: Monoid[L]
   def empty[A]: EitherT[F, L, A] = EitherT(F.pure(Either.left(L.empty)))
 }
+*/
 
 /* TODO violates right absorbtion, right distributivity, and left distributivity -- re-enable when MonadCombine laws are split in to weak/strong
 private[data] trait EitherTMonadCombine[F[_], L] extends MonadCombine[EitherT[F, L, ?]] with EitherTMonadFilter[F, L] with EitherTSemigroupK[F, L] {
diff --git a/js/src/test/scala/cats/tests/FutureTests.scala b/js/src/test/scala/cats/tests/FutureTests.scala
index e248189d34..61f4c1010d 100644
--- a/js/src/test/scala/cats/tests/FutureTests.scala
+++ b/js/src/test/scala/cats/tests/FutureTests.scala
@@ -2,10 +2,11 @@ package cats
 package js
 package tests
 
+import cats.kernel.laws.GroupLaws
 import cats.laws.discipline._
 import cats.js.instances.Await
 import cats.js.instances.future.futureComonad
-import cats.tests.CatsSuite
+import cats.tests.{CatsSuite, ListWrapper}
 
 import scala.concurrent.Future
 import scala.concurrent.duration._
@@ -54,4 +55,11 @@ class FutureTests extends CatsSuite {
   checkAll("Future[Int]", MonadErrorTests[Future, Throwable].monadError[Int, Int, Int])
   checkAll("Future[Int]", ComonadTests[Future].comonad[Int, Int, Int])
   checkAll("Future", MonadTests[Future].monad[Int, Int, Int])
+
+  {
+    implicit val F = ListWrapper.semigroup[Int]
+    checkAll("Future[ListWrapper[Int]]", GroupLaws[Future[ListWrapper[Int]]].semigroup)
+  }
+
+  checkAll("Future[Int]", GroupLaws[Future[Int]].monoid)
 }
diff --git a/jvm/src/test/scala/cats/tests/FutureTests.scala b/jvm/src/test/scala/cats/tests/FutureTests.scala
index 669d065500..4b72eb8bc1 100644
--- a/jvm/src/test/scala/cats/tests/FutureTests.scala
+++ b/jvm/src/test/scala/cats/tests/FutureTests.scala
@@ -2,9 +2,10 @@ package cats
 package jvm
 package tests
 
+import cats.kernel.laws.GroupLaws
 import cats.laws.discipline._
 import cats.laws.discipline.arbitrary._
-import cats.tests.CatsSuite
+import cats.tests.{CatsSuite, ListWrapper}
 
 import scala.concurrent.{Await, Future}
 import scala.concurrent.duration._
@@ -36,4 +37,11 @@ class FutureTests extends CatsSuite {
 
   checkAll("Future with Throwable", MonadErrorTests[Future, Throwable].monadError[Int, Int, Int])
   checkAll("Future", MonadTests[Future].monad[Int, Int, Int])
+
+  {
+    implicit val F = ListWrapper.semigroup[Int]
+    checkAll("Future[ListWrapper[Int]]", GroupLaws[Future[ListWrapper[Int]]].semigroup)
+  }
+
+  checkAll("Future[Int]", GroupLaws[Future[Int]].monoid)
 }
diff --git a/tests/src/test/scala/cats/tests/ConstTests.scala b/tests/src/test/scala/cats/tests/ConstTests.scala
index 792676ffb2..c79cbeb0a0 100644
--- a/tests/src/test/scala/cats/tests/ConstTests.scala
+++ b/tests/src/test/scala/cats/tests/ConstTests.scala
@@ -48,6 +48,9 @@ class ConstTests extends CatsSuite {
   checkAll("Const[?, ?]", BifoldableTests[Const].bifoldable[Int, Int, Int])
   checkAll("Bifoldable[Const]", SerializableTests.serializable(Bifoldable[Const]))
 
+  checkAll("InvariantMonoidal[Const[String, ?]]", InvariantMonoidalTests[Const[String, ?]].invariantMonoidal[Int, Int, Int])
+  checkAll("InvariantMonoidal[Const[String, ?]]", SerializableTests.serializable(InvariantMonoidal[Const[String, ?]]))
+
   test("show") {
 
     Const(1).show should === ("Const(1)")
diff --git a/tests/src/test/scala/cats/tests/EitherTTests.scala b/tests/src/test/scala/cats/tests/EitherTTests.scala
index 73312c9d12..dbe79220ce 100644
--- a/tests/src/test/scala/cats/tests/EitherTTests.scala
+++ b/tests/src/test/scala/cats/tests/EitherTTests.scala
@@ -243,6 +243,12 @@ class EitherTTests extends CatsSuite {
     }
   }
 
+  test("flatMap and flatMapF consistent") {
+    forAll { (eithert: EitherT[List, String, Int], f: Int => EitherT[List, String, Int])  =>
+      eithert.flatMap(f) should === (eithert.flatMapF(f(_).value))
+    }
+  }
+
   test("fold with Id consistent with Either fold") {
     forAll { (eithert: EitherT[Id, String, Int], f: String => Long, g: Int => Long) =>
       eithert.fold(f, g) should === (eithert.value.fold(f, g))
diff --git a/tests/src/test/scala/cats/tests/NestedTests.scala b/tests/src/test/scala/cats/tests/NestedTests.scala
index 0032ea502a..fc108bffe1 100644
--- a/tests/src/test/scala/cats/tests/NestedTests.scala
+++ b/tests/src/test/scala/cats/tests/NestedTests.scala
@@ -90,6 +90,13 @@ class NestedTests extends CatsSuite {
     checkAll("Contravariant[Nested[Show, Option, ?]]", SerializableTests.serializable(Contravariant[Nested[Show, Option, ?]]))
   }
 
+  {
+    // Apply composition
+    implicit val instance = ListWrapper.applyInstance
+    checkAll("Nested[List, ListWrapper, ?]", ApplyTests[Nested[List, ListWrapper, ?]].apply[Int, Int, Int])
+    checkAll("Apply[Nested[List, ListWrapper, ?]]", SerializableTests.serializable(Apply[Nested[List, ListWrapper, ?]]))
+  }
+
   {
     // Applicative composition
     implicit val instance = ListWrapper.applicative
diff --git a/tests/src/test/scala/cats/tests/TryTests.scala b/tests/src/test/scala/cats/tests/TryTests.scala
index 3548372aa4..7fe11c3293 100644
--- a/tests/src/test/scala/cats/tests/TryTests.scala
+++ b/tests/src/test/scala/cats/tests/TryTests.scala
@@ -1,6 +1,7 @@
 package cats
 package tests
 
+import cats.kernel.laws.GroupLaws
 import cats.laws.{ApplicativeLaws, CoflatMapLaws, FlatMapLaws, MonadLaws}
 import cats.laws.discipline._
 import cats.laws.discipline.arbitrary._
@@ -25,6 +26,16 @@ class TryTests extends CatsSuite {
   checkAll("Try", MonadTests[Try].monad[Int, Int, Int])
   checkAll("Monad[Try]", SerializableTests.serializable(Monad[Try]))
 
+  {
+    implicit val F = ListWrapper.semigroup[Int]
+
+    checkAll("Try[ListWrapper[Int]]", GroupLaws[Try[ListWrapper[Int]]].semigroup)
+    checkAll("Semigroup[Try[ListWrapper[Int]]", SerializableTests.serializable(Semigroup[Try[ListWrapper[Int]]]))
+  }
+
+  checkAll("Try[Int]", GroupLaws[Try[Int]].monoid)
+  checkAll("Monoid[Try[Int]]", SerializableTests.serializable(Monoid[Try[Int]]))
+
   test("show") {
     forAll { fs: Try[String] =>
       fs.show should === (fs.toString)
diff --git a/tests/src/test/scala/cats/tests/Tuple2KTests.scala b/tests/src/test/scala/cats/tests/Tuple2KTests.scala
index 9b7c993e39..ba0605c9d9 100644
--- a/tests/src/test/scala/cats/tests/Tuple2KTests.scala
+++ b/tests/src/test/scala/cats/tests/Tuple2KTests.scala
@@ -65,6 +65,13 @@ class Tuple2KTests extends CatsSuite {
     checkAll("Traverse[Tuple2K[ListWrapper, ListWrapper, ?]]", SerializableTests.serializable(Traverse[Tuple2K[ListWrapper, ListWrapper, ?]]))
   }
 
+  {
+    implicit val alternative = ListWrapper.alternative
+    implicit val iso = CartesianTests.Isomorphisms.invariant[Tuple2K[ListWrapper, ListWrapper, ?]]
+    checkAll("Tuple2K[ListWrapper, ListWrapper, ?]", AlternativeTests[Tuple2K[ListWrapper, ListWrapper, ?]].alternative[Int, Int, Int])
+    checkAll("Alternative[Tuple2K[ListWrapper, ListWrapper, ?]]", SerializableTests.serializable(Alternative[Tuple2K[ListWrapper, ListWrapper, ?]]))
+  }
+
   {
     implicit val monadCombine = ListWrapper.monadCombine
     implicit val iso = CartesianTests.Isomorphisms.invariant[Tuple2K[ListWrapper, ListWrapper, ?]]