diff --git a/core/src/main/scala/cats/syntax/flatMap.scala b/core/src/main/scala/cats/syntax/flatMap.scala
index 7161c11b2cd..f4d6c0653ca 100644
--- a/core/src/main/scala/cats/syntax/flatMap.scala
+++ b/core/src/main/scala/cats/syntax/flatMap.scala
@@ -21,7 +21,24 @@ class FlatMapOps[F[_], A](fa: F[A])(implicit F: FlatMap[F]) {
   def flatMap[B](f: A => F[B]): F[B] = F.flatMap(fa)(f)
   def mproduct[B](f: A => F[B]): F[(A, B)] = F.mproduct(fa)(f)
   def >>=[B](f: A => F[B]): F[B] = F.flatMap(fa)(f)
-  def >>[B](fb: F[B]): F[B] = F.flatMap(fa)(_ => fb)
+
+  /** Alias for [[andAfter]]. */
+  @inline final def >> [B](fb: F[B]): F[B] = andAfter(fb)
+
+  /** Sequentially compose two actions, discarding any value produced by the first. */
+  def andAfter[B](fb: F[B]): F[B] = F.flatMap(fa)(_ => fb)
+
+  /**
+   * Sequentially compose two actions, discarding any value produced by the first. This overload also lets you
+   * define the evaluation strategy of the second action. For instance you can evaluate it only ''after''
+   * the first action has finished:
+   *
+   * {{{
+   *   fa.andAfterEval(later(fb))
+   * }}}
+   */
+  def andAfterEval[B](fb: Eval[F[B]]): F[B] = F.flatMap(fa)(_ => fb.value)
+
 }
 
 class FlattenOps[F[_], A](ffa: F[F[A]])(implicit F: FlatMap[F]) {