diff --git a/laws/src/main/scala/cats/laws/NonEmptyParallelLaws.scala b/laws/src/main/scala/cats/laws/NonEmptyParallelLaws.scala
index 96deeb8df0..880b3ba1d9 100644
--- a/laws/src/main/scala/cats/laws/NonEmptyParallelLaws.scala
+++ b/laws/src/main/scala/cats/laws/NonEmptyParallelLaws.scala
@@ -4,8 +4,9 @@ package laws
 /**
  * Laws that must be obeyed by any `cats.NonEmptyParallel`.
  */
-trait NonEmptyParallelLaws[M[_], F[_]] {
-  def P: NonEmptyParallel.Aux[M, F]
+trait NonEmptyParallelLaws[M[_]] {
+  val P: NonEmptyParallel[M]
+  type F[A] = P.F[A]
 
   def parallelRoundTrip[A](ma: M[A]): IsEq[M[A]] =
     P.sequential(P.parallel(ma)) <-> ma
@@ -18,6 +19,11 @@ trait NonEmptyParallelLaws[M[_], F[_]] {
 }
 
 object NonEmptyParallelLaws {
-  def apply[M[_], F[_]](implicit ev: NonEmptyParallel.Aux[M, F]): NonEmptyParallelLaws[M, F] =
-    new NonEmptyParallelLaws[M, F] { def P: NonEmptyParallel.Aux[M, F] = ev }
+  type Aux[M[_], F0[_]] = NonEmptyParallelLaws[M] { type F[A] = F0[A]; val P: NonEmptyParallel.Aux[M, F0] }
+
+  def apply[M[_]](implicit ev: NonEmptyParallel[M]): NonEmptyParallelLaws.Aux[M, ev.F] =
+    apply[M, ev.F](ev, implicitly)
+
+  def apply[M[_], F[_]](implicit ev: NonEmptyParallel.Aux[M, F], D: DummyImplicit): NonEmptyParallelLaws.Aux[M, F] =
+    new NonEmptyParallelLaws[M] { val P: ev.type = ev }
 }
diff --git a/laws/src/main/scala/cats/laws/ParallelLaws.scala b/laws/src/main/scala/cats/laws/ParallelLaws.scala
index 892ca79eae..4e7165e94a 100644
--- a/laws/src/main/scala/cats/laws/ParallelLaws.scala
+++ b/laws/src/main/scala/cats/laws/ParallelLaws.scala
@@ -4,14 +4,19 @@ package laws
 /**
  * Laws that must be obeyed by any `cats.Parallel`.
  */
-trait ParallelLaws[M[_], F[_]] extends NonEmptyParallelLaws[M, F] {
-  def P: Parallel.Aux[M, F]
+trait ParallelLaws[M[_]] extends NonEmptyParallelLaws[M] {
+  val P: Parallel[M]
 
   def isomorphicPure[A](a: A): IsEq[F[A]] =
     P.applicative.pure(a) <-> P.parallel(P.monad.pure(a))
 }
 
 object ParallelLaws {
-  def apply[M[_], F[_]](implicit ev: Parallel.Aux[M, F]): ParallelLaws[M, F] =
-    new ParallelLaws[M, F] { def P: Parallel.Aux[M, F] = ev }
+  type Aux[M[_], F0[_]] = ParallelLaws[M] { type F[A] = F0[A]; val P: Parallel.Aux[M, F0] }
+
+  def apply[M[_]](implicit ev: Parallel[M]): ParallelLaws.Aux[M, ev.F] =
+    apply[M, ev.F](ev, implicitly)
+
+  def apply[M[_], F[_]](implicit ev: Parallel.Aux[M, F], D: DummyImplicit): ParallelLaws.Aux[M, F] =
+    new ParallelLaws[M] { val P: ev.type = ev }
 }
diff --git a/laws/src/main/scala/cats/laws/discipline/NonEmptyParallelTests.scala b/laws/src/main/scala/cats/laws/discipline/NonEmptyParallelTests.scala
index 64b14b8c3f..b503b3329b 100644
--- a/laws/src/main/scala/cats/laws/discipline/NonEmptyParallelTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/NonEmptyParallelTests.scala
@@ -6,8 +6,9 @@ import org.scalacheck.Arbitrary
 import org.scalacheck.Prop.forAll
 import org.typelevel.discipline.Laws
 
-trait NonEmptyParallelTests[M[_], F[_]] extends Laws {
-  def laws: NonEmptyParallelLaws[M, F]
+trait NonEmptyParallelTests[M[_]] extends Laws {
+  val laws: NonEmptyParallelLaws[M]
+  type F[A] = laws.F[A]
 
   def nonEmptyParallel[A, B](implicit ArbA: Arbitrary[A],
                              ArbM: Arbitrary[M[A]],
@@ -27,6 +28,11 @@ trait NonEmptyParallelTests[M[_], F[_]] extends Laws {
 }
 
 object NonEmptyParallelTests {
-  def apply[M[_], F[_]](implicit ev: NonEmptyParallel.Aux[M, F]): NonEmptyParallelTests[M, F] =
-    new NonEmptyParallelTests[M, F] { val laws: NonEmptyParallelLaws[M, F] = NonEmptyParallelLaws[M, F] }
+  type Aux[M[_], F0[_]] = NonEmptyParallelTests[M] { type F[A] = F0[A]; val laws: NonEmptyParallelLaws.Aux[M, F0] }
+
+  def apply[M[_]](implicit ev: NonEmptyParallel[M]): NonEmptyParallelTests.Aux[M, ev.F] =
+    apply[M, ev.F](ev, implicitly)
+
+  def apply[M[_], F[_]](implicit ev: NonEmptyParallel.Aux[M, F], D: DummyImplicit): NonEmptyParallelTests.Aux[M, F] =
+    new NonEmptyParallelTests[M] { val laws = NonEmptyParallelLaws[M] }
 }
diff --git a/laws/src/main/scala/cats/laws/discipline/ParallelTests.scala b/laws/src/main/scala/cats/laws/discipline/ParallelTests.scala
index b5b394adc7..5f4e28fa87 100644
--- a/laws/src/main/scala/cats/laws/discipline/ParallelTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/ParallelTests.scala
@@ -5,8 +5,8 @@ package discipline
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop.forAll
 
-trait ParallelTests[M[_], F[_]] extends NonEmptyParallelTests[M, F] {
-  def laws: ParallelLaws[M, F]
+trait ParallelTests[M[_]] extends NonEmptyParallelTests[M] {
+  val laws: ParallelLaws[M]
 
   def parallel[A, B](implicit ArbA: Arbitrary[A],
                      ArbM: Arbitrary[M[A]],
@@ -24,6 +24,11 @@ trait ParallelTests[M[_], F[_]] extends NonEmptyParallelTests[M, F] {
 }
 
 object ParallelTests {
-  def apply[M[_], F[_]](implicit ev: Parallel.Aux[M, F]): ParallelTests[M, F] =
-    new ParallelTests[M, F] { val laws: ParallelLaws[M, F] = ParallelLaws[M, F] }
+  type Aux[M[_], F0[_]] = ParallelTests[M] { type F[A] = F0[A]; val laws: ParallelLaws.Aux[M, F0] }
+
+  def apply[M[_]](implicit ev: Parallel[M]): ParallelTests.Aux[M, ev.F] =
+    apply[M, ev.F](ev, implicitly)
+
+  def apply[M[_], F[_]](implicit ev: Parallel.Aux[M, F], D: DummyImplicit): ParallelTests.Aux[M, F] =
+    new ParallelTests[M] { val laws = ParallelLaws[M] }
 }
diff --git a/tests/src/test/scala-2.13+/cats/tests/ScalaVersionSpecific.scala b/tests/src/test/scala-2.13+/cats/tests/ScalaVersionSpecific.scala
index cfc4ce7437..43c3230dd9 100644
--- a/tests/src/test/scala-2.13+/cats/tests/ScalaVersionSpecific.scala
+++ b/tests/src/test/scala-2.13+/cats/tests/ScalaVersionSpecific.scala
@@ -1,7 +1,7 @@
 package cats
 package tests
 
-import cats.data.{NonEmptyLazyList, OneAnd, ZipLazyList}
+import cats.data.NonEmptyLazyList
 import cats.instances.lazyList._
 import cats.laws.discipline.{NonEmptyParallelTests, ParallelTests}
 import cats.laws.discipline.arbitrary._
@@ -123,11 +123,11 @@ trait ScalaVersionSpecificParallelSuite { self: ParallelSuite =>
   }
 
   // Can't test Parallel here, as Applicative[ZipLazyList].pure doesn't terminate
-  checkAll("Parallel[LazyList, ZipLazyList]",
-           NonEmptyParallelTests[LazyList, ZipLazyList].nonEmptyParallel[Int, String])
+  checkAll("Parallel[LazyList]",
+           NonEmptyParallelTests[LazyList].nonEmptyParallel[Int, String])
 
-  checkAll("Parallel[NonEmptyLazyList, OneAnd[ZipLazyList, *]]",
-           ParallelTests[NonEmptyLazyList, OneAnd[ZipLazyList, *]].parallel[Int, String])
+  checkAll("Parallel[NonEmptyLazyList]",
+           ParallelTests[NonEmptyLazyList].parallel[Int, String])
 }
 
 trait ScalaVersionSpecificRegressionSuite { self: RegressionSuite =>
diff --git a/tests/src/test/scala/cats/tests/ParallelSuite.scala b/tests/src/test/scala/cats/tests/ParallelSuite.scala
index 4f385de2c2..d1b4168aac 100644
--- a/tests/src/test/scala/cats/tests/ParallelSuite.scala
+++ b/tests/src/test/scala/cats/tests/ParallelSuite.scala
@@ -3,7 +3,6 @@ package tests
 
 import cats._
 import cats.data.NonEmptyList.ZipNonEmptyList
-import cats.data.NonEmptyVector.ZipNonEmptyVector
 import cats.data._
 import org.scalatest.funsuite.AnyFunSuiteLike
 import cats.laws.discipline.{ApplicativeErrorTests, MiniInt, NonEmptyParallelTests, ParallelTests, SerializableTests}
@@ -416,63 +415,55 @@ class ParallelSuite extends CatsSuite with ApplicativeErrorForEitherTest with Sc
     resultWithInstance should ===("parallel".some)
   }
 
-  checkAll("Parallel[Either[String, *], Validated[String, *]]",
-           ParallelTests[Either[String, *], Validated[String, *]].parallel[Int, String])
-  checkAll("Parallel[Ior[String, *], Ior[String, *]]",
-           ParallelTests[Ior[String, *], Ior[String, *]].parallel[Int, String])
+  checkAll("Parallel[Either[String, *]", ParallelTests[Either[String, *]].parallel[Int, String])
+  checkAll("Parallel[Ior[String, *]]", ParallelTests[Ior[String, *]].parallel[Int, String])
   checkAll(
-    "Parallel[IorT[F, String, *], IorT[F, String, *]] with parallel effect",
-    ParallelTests[IorT[Either[String, *], String, *], IorT[Validated[String, *], String, *]].parallel[Int, String]
+    "Parallel[IorT[F, String, *]] with parallel effect",
+    ParallelTests[IorT[Either[String, *], String, *]].parallel[Int, String]
   )
   checkAll(
-    "Parallel[IorT[F, String, *], IorT[F, String, *]] with sequential effect",
-    ParallelTests[IorT[Option, String, *], IorT[Option, String, *]].parallel[Int, String]
+    "Parallel[IorT[F, String, *]] with sequential effect",
+    ParallelTests[IorT[Option, String, *]].parallel[Int, String]
   )
-  checkAll("Parallel[OptionT[M, *], Nested[F, Option, *]]",
-           ParallelTests[OptionT[Either[String, *], *], Nested[Validated[String, *], Option, *]].parallel[Int, String])
+  checkAll("Parallel[OptionT[M, *]]", ParallelTests[OptionT[Either[String, *], *]].parallel[Int, String])
   checkAll(
-    "Parallel[EitherT[M, String, *], Nested[F, Validated[String, *], *]]",
-    ParallelTests[EitherT[Either[String, *], String, *], Nested[Validated[String, *], Validated[String, *], *]]
+    "Parallel[EitherT[M, String, *]]",
+    ParallelTests[EitherT[Either[String, *], String, *]]
       .parallel[Int, String]
   )
   checkAll(
-    "Parallel[EitherT[Option, String, *], Nested[Option, Validated[String, *], *]]",
-    ParallelTests[EitherT[Option, String, *], Nested[Option, Validated[String, *], *]].parallel[Int, String]
+    "Parallel[EitherT[Option, String, *]]",
+    ParallelTests[EitherT[Option, String, *]].parallel[Int, String]
   )
   checkAll(
-    "Parallel[WriterT[M, Int, *], WriterT[F, Int, *]]",
-    ParallelTests[WriterT[Either[String, *], Int, *], WriterT[Validated[String, *], Int, *]].parallel[Int, String]
+    "Parallel[WriterT[M, Int, *]]",
+    ParallelTests[WriterT[Either[String, *], Int, *]].parallel[Int, String]
   )
-  checkAll("NonEmptyParallel[Vector, ZipVector]",
-           NonEmptyParallelTests[Vector, ZipVector].nonEmptyParallel[Int, String])
-  checkAll("NonEmptyParallel[List, ZipList]", NonEmptyParallelTests[List, ZipList].nonEmptyParallel[Int, String])
+  checkAll("NonEmptyParallel[Vector]", NonEmptyParallelTests[Vector].nonEmptyParallel[Int, String])
+  checkAll("NonEmptyParallel[List]", NonEmptyParallelTests[List].nonEmptyParallel[Int, String])
   // Can't test Parallel here, as Applicative[ZipStream].pure doesn't terminate
-  checkAll("Parallel[Stream, ZipStream]", NonEmptyParallelTests[Stream, ZipStream].nonEmptyParallel[Int, String])
+  checkAll("Parallel[Stream]", NonEmptyParallelTests[Stream].nonEmptyParallel[Int, String])
 
-  checkAll("NonEmptyParallel[NonEmptyVector, ZipNonEmptyVector]",
-           NonEmptyParallelTests[NonEmptyVector, ZipNonEmptyVector].nonEmptyParallel[Int, String])
+  checkAll("NonEmptyParallel[NonEmptyVector]", NonEmptyParallelTests[NonEmptyVector].nonEmptyParallel[Int, String])
 
-  checkAll("NonEmptyParallel[NonEmptyList, ZipNonEmptyList]",
-           NonEmptyParallelTests[NonEmptyList, ZipNonEmptyList].nonEmptyParallel[Int, String])
+  checkAll("NonEmptyParallel[NonEmptyList]", NonEmptyParallelTests[NonEmptyList].nonEmptyParallel[Int, String])
 
-  checkAll("Parallel[NonEmptyStream, OneAnd[ZipStream, *]",
-           ParallelTests[NonEmptyStream, OneAnd[ZipStream, *]].parallel[Int, String])
+  // TODO this doesn't infer?
+  checkAll("Parallel[NonEmptyStream]", ParallelTests[NonEmptyStream, OneAnd[ZipStream, *]].parallel[Int, String])
 
-  checkAll("Parallel[Id, Id]", ParallelTests[Id, Id].parallel[Int, String])
+  checkAll("Parallel[Id]", ParallelTests[Id].parallel[Int, String])
 
-  checkAll("NonEmptyParallel[NonEmptyList, ZipNonEmptyList]",
-           SerializableTests.serializable(NonEmptyParallel[NonEmptyList, ZipNonEmptyList]))
+  checkAll("NonEmptyParallel[NonEmptyList]", SerializableTests.serializable(NonEmptyParallel[NonEmptyList]))
 
-  checkAll("Parallel[Either[String, *], Validated[String, *]]",
-           SerializableTests.serializable(Parallel[Either[String, *], Validated[String, *]]))
+  checkAll("Parallel[Either[String, *]]", SerializableTests.serializable(Parallel[Either[String, *]]))
 
   {
     implicit def kleisliEq[F[_], A, B](implicit ev: Eq[A => F[B]]): Eq[Kleisli[F, A, B]] =
       Eq.by[Kleisli[F, A, B], A => F[B]](_.run)
 
     checkAll(
-      "Parallel[KleisliT[M, A, *], Kleisli[F, A, *]]",
-      ParallelTests[Kleisli[Either[String, *], MiniInt, *], Kleisli[Validated[String, *], MiniInt, *]]
+      "Parallel[KleisliT[M, A, *]]",
+      ParallelTests[Kleisli[Either[String, *], MiniInt, *]]
         .parallel[Int, String]
     )
   }