diff --git a/core/src/main/scala/cats/Reducible.scala b/core/src/main/scala/cats/Reducible.scala
index 20a38bf1ae..2f92905e38 100644
--- a/core/src/main/scala/cats/Reducible.scala
+++ b/core/src/main/scala/cats/Reducible.scala
@@ -97,7 +97,7 @@ import simulacrum.typeclass
    * that we only need `Apply[G]` here, since we don't need to call
    * `Applicative#pure` for a starting value.
    */
-  def sequence1_[G[_], A, B](fga: F[G[A]])(implicit G: Apply[G]): G[Unit] =
+  def sequence1_[G[_], A](fga: F[G[A]])(implicit G: Apply[G]): G[Unit] =
     G.map(reduceLeft(fga)((x, y) => G.map2(x, y)((_, b) => b)))(_ => ())
 
   /**
diff --git a/laws/src/main/scala/cats/laws/ReducibleLaws.scala b/laws/src/main/scala/cats/laws/ReducibleLaws.scala
index 5075a97ab6..937a23c35d 100644
--- a/laws/src/main/scala/cats/laws/ReducibleLaws.scala
+++ b/laws/src/main/scala/cats/laws/ReducibleLaws.scala
@@ -21,6 +21,12 @@ trait ReducibleLaws[F[_]] extends FoldableLaws[F] {
     B: Semigroup[B]
   ): IsEq[B] =
     fa.reduceMap(f) <-> fa.reduceRightTo(f)((a, eb) => eb.map(f(a) |+| _)).value
+
+  def traverseConsistent[G[_]: Applicative, A, B](fa: F[A], f: A => G[B]): IsEq[G[Unit]] =
+    fa.traverse1_(f) <-> fa.traverse_(f)
+
+  def sequenceConsistent[G[_]: Applicative, A](fa: F[G[A]]): IsEq[G[Unit]] =
+    fa.sequence1_ <-> fa.sequence_
 }
 
 object ReducibleLaws {
diff --git a/laws/src/main/scala/cats/laws/discipline/ReducibleTests.scala b/laws/src/main/scala/cats/laws/discipline/ReducibleTests.scala
index cb1f343aa6..4f7db2d858 100644
--- a/laws/src/main/scala/cats/laws/discipline/ReducibleTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/ReducibleTests.scala
@@ -8,16 +8,21 @@ import org.scalacheck.Prop.forAll
 trait ReducibleTests[F[_]] extends FoldableTests[F] {
   def laws: ReducibleLaws[F]
 
-  def reducible[A: Arbitrary, B: Arbitrary](implicit
+  def reducible[G[_]: Applicative, A: Arbitrary, B: Arbitrary](implicit
     ArbFA: Arbitrary[F[A]],
+    ArbFGA: Arbitrary[F[G[A]]],
+    ArbGB: Arbitrary[G[B]],
     B: Monoid[B],
+    EqG: Eq[G[Unit]],
     EqB: Eq[B]
   ): RuleSet =
     new DefaultRuleSet(
       name = "reducible",
       parent = Some(foldable[A, B]),
       "reduceLeftTo consistent with reduceMap" -> forAll(laws.reduceLeftToConsistentWithReduceMap[A, B] _),
-      "reduceRightTo consistent with reduceMap" -> forAll(laws.reduceRightToConsistentWithReduceMap[A, B] _)
+      "reduceRightTo consistent with reduceMap" -> forAll(laws.reduceRightToConsistentWithReduceMap[A, B] _),
+      "traverse1_ consistent with traverse_" -> forAll(laws.traverseConsistent[G, A, B] _),
+      "sequence1_ consistent with sequence_" -> forAll(laws.sequenceConsistent[G, A] _)
     )
 }
 
diff --git a/tests/src/test/scala/cats/tests/OneAndTests.scala b/tests/src/test/scala/cats/tests/OneAndTests.scala
index 29768816ed..ad711ea410 100644
--- a/tests/src/test/scala/cats/tests/OneAndTests.scala
+++ b/tests/src/test/scala/cats/tests/OneAndTests.scala
@@ -5,16 +5,20 @@ import algebra.laws.{GroupLaws, OrderLaws}
 
 import cats.data.{NonEmptyList, OneAnd}
 import cats.laws.discipline.{ComonadTests, FunctorTests, SemigroupKTests, FoldableTests, MonadTests, SerializableTests, CartesianTests, TraverseTests, ReducibleTests}
-import cats.laws.discipline.arbitrary.oneAndArbitrary
+import cats.laws.discipline.arbitrary._
 import cats.laws.discipline.eq._
 
 class OneAndTests extends CatsSuite {
+  // Lots of collections here.. telling ScalaCheck to calm down a bit
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    PropertyCheckConfig(maxSize = 5, minSuccessful = 20)
+
   checkAll("OneAnd[List, Int]", OrderLaws[OneAnd[List, Int]].eqv)
 
   checkAll("OneAnd[List, Int] with Option", TraverseTests[OneAnd[List, ?]].traverse[Int, Int, Int, Int, Option, Option])
   checkAll("Traverse[OneAnd[List, A]]", SerializableTests.serializable(Traverse[OneAnd[List, ?]]))
 
-  checkAll("OneAnd[List, Int]", ReducibleTests[OneAnd[List, ?]].reducible[Int, Int])
+  checkAll("OneAnd[List, Int]", ReducibleTests[OneAnd[List, ?]].reducible[Option, Int, Int])
   checkAll("Reducible[OneAnd[List, ?]]", SerializableTests.serializable(Reducible[OneAnd[List, ?]]))
 
   implicit val iso = CartesianTests.Isomorphisms.invariant[OneAnd[ListWrapper, ?]](OneAnd.oneAndFunctor(ListWrapper.functor))
@@ -117,4 +121,46 @@ class OneAndTests extends CatsSuite {
       nel.map(p).unwrap should === (list.map(p))
     }
   }
+
+  test("reduceLeft consistent with foldLeft") {
+    forAll { (nel: NonEmptyList[Int], f: (Int, Int) => Int) =>
+      nel.reduceLeft(f) should === (nel.tail.foldLeft(nel.head)(f))
+    }
+  }
+
+  test("reduceRight consistent with foldRight") {
+    forAll { (nel: NonEmptyList[Int], f: (Int, Eval[Int]) => Eval[Int]) =>
+      nel.reduceRight(f).value should === (nel.tail.foldRight(nel.head)((a, b) => f(a, Now(b)).value))
+    }
+  }
+
+  test("reduce consistent with fold") {
+    forAll { (nel: NonEmptyList[Int]) =>
+      nel.reduce should === (nel.fold)
+    }
+  }
+
+  test("reduce consistent with reduceK") {
+    forAll { (nel: NonEmptyList[Option[Int]]) =>
+      nel.reduce(SemigroupK[Option].algebra[Int]) should === (nel.reduceK)
+    }
+  }
+
+  test("reduceLeftToOption consistent with foldLeft + Option") {
+    forAll { (nel: NonEmptyList[Int], f: Int => String, g: (String, Int) => String) =>
+      val expected = nel.tail.foldLeft(Option(f(nel.head))) { (opt, i) =>
+        opt.map(s => g(s, i))
+      }
+      nel.reduceLeftToOption(f)(g) should === (expected)
+    }
+  }
+
+  test("reduceRightToOption consistent with foldRight + Option") {
+    forAll { (nel: NonEmptyList[Int], f: Int => String, g: (Int, Eval[String]) => Eval[String]) =>
+      val expected = nel.tail.foldRight(Option(f(nel.head))) { (i, opt) =>
+        opt.map(s => g(i, Now(s)).value)
+      }
+      nel.reduceRightToOption(f)(g).value should === (expected)
+    }
+  }
 }
diff --git a/tests/src/test/scala/cats/tests/ReducibleTests.scala b/tests/src/test/scala/cats/tests/ReducibleTests.scala
new file mode 100644
index 0000000000..d834a99e02
--- /dev/null
+++ b/tests/src/test/scala/cats/tests/ReducibleTests.scala
@@ -0,0 +1,18 @@
+package cats
+package tests
+
+import cats.data.{NonEmptyList, NonEmptyVector}
+import cats.laws.discipline.{ReducibleTests, SerializableTests}
+import cats.laws.discipline.arbitrary.oneAndArbitrary
+
+class ReducibleTest extends CatsSuite {
+  // Lots of collections here.. telling ScalaCheck to calm down a bit
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    PropertyCheckConfig(maxSize = 5, minSuccessful = 20)
+
+  type NEVL[A] = NonEmptyList[NonEmptyVector[A]]
+  val nevlReducible: Reducible[NEVL] =
+    Reducible[NonEmptyList].compose[NonEmptyVector]
+  checkAll("NonEmptyList compose NonEmptyVector", ReducibleTests(nevlReducible).reducible[Option, Int, String])
+  checkAll("Reducible[NonEmptyList compose NonEmptyVector]", SerializableTests.serializable(nevlReducible))
+}