diff --git a/alleycats-core/src/main/scala/alleycats/std/set.scala b/alleycats-core/src/main/scala/alleycats/std/set.scala
index 9421e69aac..bff022b424 100644
--- a/alleycats-core/src/main/scala/alleycats/std/set.scala
+++ b/alleycats-core/src/main/scala/alleycats/std/set.scala
@@ -55,8 +55,16 @@ trait SetInstances {
   // If we accept Monad for Set, we can also have Alternative, as
   // Alternative only requires MonoidK (already accepted by cats-core) and
   // the Applicative that comes from Monad.
-  implicit val alleyCatsStdSetMonad: Monad[Set] with Alternative[Set] =
-    new Monad[Set] with Alternative[Set] {
+  implicit val alleycatsStdInstancesForSet
+    : Monad[Set] with Alternative[Set] with Traverse[Set] with TraverseFilter[Set] =
+    new Monad[Set] with Alternative[Set] with Traverse[Set] with TraverseFilter[Set] {
+      val traverse: Traverse[Set] = this
+
+      def traverseFilter[G[_], A, B](fa: Set[A])(f: A => G[Option[B]])(implicit G: Applicative[G]): G[Set[B]] =
+        traverse
+          .foldRight(fa, Eval.now(G.pure(Set.empty[B])))((x, xse) => G.map2Eval(f(x), xse)((i, o) => i.fold(o)(o + _)))
+          .value
+
       def pure[A](a: A): Set[A] = Set(a)
       override def map[A, B](fa: Set[A])(f: A => B): Set[B] = fa.map(f)
       def flatMap[A, B](fa: Set[A])(f: A => Set[B]): Set[B] = fa.flatMap(f)
@@ -98,13 +106,7 @@ trait SetInstances {
       override def prependK[A](a: A, fa: Set[A]): Set[A] = fa + a
 
       override def appendK[A](fa: Set[A], a: A): Set[A] = fa + a
-    }
 
-  // Since iteration order is not guaranteed for sets, folds and other
-  // traversals may produce different results for input sets which
-  // appear to be the same.
-  implicit val alleyCatsSetTraverse: Traverse[Set] =
-    new Traverse[Set] {
       def foldLeft[A, B](fa: Set[A], b: B)(f: (B, A) => B): B =
         fa.foldLeft(b)(f)
       def foldRight[A, B](fa: Set[A], lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] =
@@ -173,13 +175,10 @@ trait SetInstances {
         fa.collectFirst(Function.unlift(f))
     }
 
-  implicit val alleyCatsSetTraverseFilter: TraverseFilter[Set] =
-    new TraverseFilter[Set] {
-      val traverse: Traverse[Set] = alleyCatsSetTraverse
-
-      def traverseFilter[G[_], A, B](fa: Set[A])(f: A => G[Option[B]])(implicit G: Applicative[G]): G[Set[B]] =
-        traverse
-          .foldRight(fa, Eval.now(G.pure(Set.empty[B])))((x, xse) => G.map2Eval(f(x), xse)((i, o) => i.fold(o)(o + _)))
-          .value
-    }
+  @deprecated("Use alleycatsStdInstancesForSet", "2.13.0")
+  val alleyCatsSetTraverse: Traverse[Set] = alleycatsStdInstancesForSet
+  @deprecated("Use alleycatsStdInstancesForSet", "2.13.0")
+  val alleyCatsStdSetMonad: Monad[Set] with Alternative[Set] = alleycatsStdInstancesForSet
+  @deprecated("Use alleycatsStdInstancesForSet", "2.13.0")
+  val alleyCatsSetTraverseFilter: TraverseFilter[Set] = alleycatsStdInstancesForSet
 }
diff --git a/alleycats-laws/shared/src/test/scala/alleycats/tests/SetSuite.scala b/alleycats-laws/shared/src/test/scala/alleycats/tests/SetSuite.scala
index c71091bc78..8b926b34c9 100644
--- a/alleycats-laws/shared/src/test/scala/alleycats/tests/SetSuite.scala
+++ b/alleycats-laws/shared/src/test/scala/alleycats/tests/SetSuite.scala
@@ -28,10 +28,10 @@ import cats.instances.all._
 import cats.kernel.laws.discipline.SerializableTests
 import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import cats.laws.discipline.arbitrary._
-import cats.laws.discipline.{AlternativeTests, ShortCircuitingTests, TraverseFilterTests}
+import cats.laws.discipline.{AlternativeTests, FunctorTests, ShortCircuitingTests, TraverseFilterTests}
 
 class SetSuite extends AlleycatsSuite {
-  implicit val iso: Isomorphisms[Set] = Isomorphisms.invariant[Set](alleyCatsStdSetMonad)
+  implicit val iso: Isomorphisms[Set] = Isomorphisms.invariant[Set](alleycatsStdInstancesForSet)
 
   checkAll("FlatMapRec[Set]", FlatMapRecTests[Set].tailRecM[Int])
 
@@ -40,6 +40,9 @@ class SetSuite extends AlleycatsSuite {
   checkAll("TraverseFilter[Set]", TraverseFilterTests[Set].traverseFilter[Int, Int, Int])
 
   checkAll("Set[Int]", AlternativeTests[Set].alternative[Int, Int, Int])
+
+  checkAll("Functor[Int]", FunctorTests[Set].functor[Int, Int, Int])
+
   checkAll("Alternative[Set]", SerializableTests.serializable(Alternative[Set]))
 
   checkAll("Set[Int]", ShortCircuitingTests[Set].traverseFilter[Int])