diff --git a/compat/src/main/scala-2.11/scala/collection/compat/package.scala b/compat/src/main/scala-2.11/scala/collection/compat/package.scala
index bf713e54..8cdd3c38 100644
--- a/compat/src/main/scala-2.11/scala/collection/compat/package.scala
+++ b/compat/src/main/scala-2.11/scala/collection/compat/package.scala
@@ -21,6 +21,17 @@ package object compat extends compat.PackageShared {
       implicit ordering: Ordering[A]): CanBuildFrom[Any, A, CC[A]] =
     CompatImpl.simpleCBF(fact.newBuilder[A])
 
+  // CanBuildFrom instances for `IterableView[(K, V), Map[K, V]]` that preserve
+  // the strict type of the view to be `Map` instead of `Iterable`
+  // Instances produced by this method are used to chain `filterKeys` after `mapValues`
+  implicit def canBuildFromIterableViewMapLike[K, V, L, W, CC[X, Y] <: Map[X, Y]]: CanBuildFrom[IterableView[(K, V), CC[K, V]], (L, W), IterableView[(L, W), CC[L, W]]] =
+    new CanBuildFrom[IterableView[(K, V), CC[K, V]], (L, W), IterableView[(L, W), CC[L, W]]] {
+      // `CanBuildFrom` parameters are used as type constraints, they are not used
+      // at run-time, hence the dummy builder implementations
+      def apply(from: IterableView[(K, V), CC[K, V]]) = new TraversableView.NoBuilder
+      def apply() = new TraversableView.NoBuilder
+    }
+
   implicit def toTraversableLikeExtensionMethods[Repr](self: Repr)(
       implicit traversable: IsTraversableLike[Repr])
     : TraversableLikeExtensionMethods[traversable.A, Repr] =
diff --git a/compat/src/main/scala-2.11_2.12/scala/collection/compat/PackageShared.scala b/compat/src/main/scala-2.11_2.12/scala/collection/compat/PackageShared.scala
index 785fbcf4..62f6d728 100644
--- a/compat/src/main/scala-2.11_2.12/scala/collection/compat/PackageShared.scala
+++ b/compat/src/main/scala-2.11_2.12/scala/collection/compat/PackageShared.scala
@@ -354,7 +354,15 @@ class MapViewExtensionMethods[K, V, C <: scala.collection.Map[K, V]](
       implicit bf: CanBuildFrom[IterableView[(K, V), C], (K, W), That]): That =
     self.map[(K, W), That] { case (k, v) => (k, f(v)) }
 
-  def filterKeys[That](p: K => Boolean)(
-      implicit bf: CanBuildFrom[IterableView[(K, V), C], (K, V), That]): That =
-    self.collect[(K, V), That] { case (k, v) if p(k) => (k, v) }
+  // TODO: Replace the current implementation of `mapValues` with this
+  //       after major version bump when bincompat can be broken.
+  //       At the same time, remove `canBuildFromIterableViewMapLike`
+  /*
+  def mapValues[W](f: V => W): IterableView[(K, W), C] =
+    // the implementation of `self.map` also casts the result
+    self.map({ case (k, v) => (k, f(v)) }).asInstanceOf[IterableView[(K, W), C]]
+   */
+
+  def filterKeys(p: K => Boolean): IterableView[(K, V), C] =
+    self.filter { case (k, _) => p(k) }
 }
diff --git a/compat/src/main/scala-2.12/scala/collection/compat/package.scala b/compat/src/main/scala-2.12/scala/collection/compat/package.scala
index c73d66a6..012532d4 100644
--- a/compat/src/main/scala-2.12/scala/collection/compat/package.scala
+++ b/compat/src/main/scala-2.12/scala/collection/compat/package.scala
@@ -32,6 +32,17 @@ package object compat extends compat.PackageShared {
       implicit ordering: Ordering[A]): CanBuildFrom[Any, A, CC[A]] =
     CompatImpl.simpleCBF(fact.newBuilder[A])
 
+  // CanBuildFrom instances for `IterableView[(K, V), Map[K, V]]` that preserve
+  // the strict type of the view to be `Map` instead of `Iterable`
+  // Instances produced by this method are used to chain `filterKeys` after `mapValues`
+  implicit def canBuildFromIterableViewMapLike[K, V, L, W, CC[X, Y] <: Map[X, Y]]: CanBuildFrom[IterableView[(K, V), CC[K, V]], (L, W), IterableView[(L, W), CC[L, W]]] =
+    new CanBuildFrom[IterableView[(K, V), CC[K, V]], (L, W), IterableView[(L, W), CC[L, W]]] {
+      // `CanBuildFrom` parameters are used as type constraints, they are not used
+      // at run-time, hence the dummy builder implementations
+      def apply(from: IterableView[(K, V), CC[K, V]]) = new TraversableView.NoBuilder
+      def apply() = new TraversableView.NoBuilder
+    }
+
   implicit def toTraversableLikeExtensionMethods[Repr](self: Repr)(
       implicit traversable: IsTraversableLike[Repr])
     : TraversableLikeExtensionMethods[traversable.A, Repr] =
diff --git a/compat/src/test/scala/test/scala/collection/ViewTest.scala b/compat/src/test/scala/test/scala/collection/ViewTest.scala
index 7c150fc4..fd28ce23 100644
--- a/compat/src/test/scala/test/scala/collection/ViewTest.scala
+++ b/compat/src/test/scala/test/scala/collection/ViewTest.scala
@@ -35,4 +35,11 @@ class ViewTest {
     assertEquals(oldStyle.toMap, newStyle.toMap)
   }
 
+  @Test
+  def filterKeysMapValues(): Unit = {
+    val m = Map("a" -> 1, "b" -> 2, "c" -> 3)
+    assertEquals(Map(), m.view.filterKeys(_.length > 1).mapValues(_ + 1).toMap)
+    assertEquals(Map(), m.view.mapValues(_ + 1).filterKeys(_.length > 1).toMap)
+  }
+
 }