diff --git a/build.sbt b/build.sbt
index f7f67baa10..c57abfeb75 100644
--- a/build.sbt
+++ b/build.sbt
@@ -248,6 +248,14 @@ def mimaSettings(moduleName: String) = Seq(
       exclude[ReversedMissingMethodProblem]("cats.NonEmptyParallel.parForEffect"),
       exclude[ReversedMissingMethodProblem]("cats.NonEmptyParallel.parFollowedBy"),
       exclude[ReversedMissingMethodProblem]("cats.syntax.ParallelSyntax.catsSyntaxParallelAp"),
+      exclude[DirectMissingMethodProblem]("cats.FlatMap.>>="),
+      exclude[DirectMissingMethodProblem]("cats.FlatMap#Ops.>>="),
+      exclude[IncompatibleMethTypeProblem]("cats.syntax.FlatMapOps.>>"),
+      exclude[IncompatibleMethTypeProblem]("cats.syntax.FlatMapOps.>>$extension"),
+      exclude[DirectMissingMethodProblem]("cats.data.IndexedStateTMonad.>>="),
+      exclude[DirectMissingMethodProblem]("cats.data.RWSTMonad.>>="),
+      exclude[DirectMissingMethodProblem]("cats.data.CokleisliMonad.>>="),
+      exclude[DirectMissingMethodProblem]("cats.instances.FlatMapTuple2.>>="),
       exclude[DirectMissingMethodProblem]("cats.Applicative.traverse"),
       exclude[DirectMissingMethodProblem]("cats.Applicative.sequence"),
       exclude[DirectMissingMethodProblem]("cats.data.IndexedStateTMonad.traverse"),
@@ -262,6 +270,7 @@ def mimaSettings(moduleName: String) = Seq(
       exclude[DirectMissingMethodProblem]("cats.data.ValidatedApplicative.sequence"),
       exclude[DirectMissingMethodProblem]("cats.data.RWSTAlternative.traverse"),
       exclude[DirectMissingMethodProblem]("cats.data.RWSTAlternative.sequence")
+
     )
   }
 )
diff --git a/core/src/main/scala/cats/FlatMap.scala b/core/src/main/scala/cats/FlatMap.scala
index 1c4b12f0f3..cec786c763 100644
--- a/core/src/main/scala/cats/FlatMap.scala
+++ b/core/src/main/scala/cats/FlatMap.scala
@@ -20,11 +20,6 @@ import simulacrum.typeclass
 @typeclass trait FlatMap[F[_]] extends Apply[F] {
   def flatMap[A, B](fa: F[A])(f: A => F[B]): F[B]
 
-  /**
-   * Alias for [[flatMap]].
-   */
-  def >>=[A, B](fa: F[A])(f: A => F[B]): F[B] = flatMap(fa)(f)
-
   /**
    * "flatten" a nested `F` of `F` structure into a single-layer `F` structure.
    *
diff --git a/core/src/main/scala/cats/syntax/flatMap.scala b/core/src/main/scala/cats/syntax/flatMap.scala
index 4342b42788..e3c8f14a5e 100644
--- a/core/src/main/scala/cats/syntax/flatMap.scala
+++ b/core/src/main/scala/cats/syntax/flatMap.scala
@@ -18,8 +18,19 @@ trait FlatMapSyntax extends FlatMap.ToFlatMapOps {
 
 final class FlatMapOps[F[_], A](val fa: F[A]) extends AnyVal {
 
-  @deprecated("Use *> instead", "1.0.0-RC1")
-  def >>[B](fb: F[B])(implicit F: FlatMap[F]): F[B] = F.followedBy(fa)(fb)
+  /**
+   * Alias for [[flatMap]].
+   */
+  def >>=[B](f: A => F[B])(implicit F: FlatMap[F]): F[B] = F.flatMap(fa)(f)
+
+  /**
+   * Alias for `fa.flatMap(_ => fb)`.
+   *
+   * Unlike `*>`, `fb` is defined as a by-name parameter, allowing this
+   * method to be used in cases where computing `fb` is not stack safe
+   * unless suspended in a `flatMap`.
+   */
+  def >>[B](fb: => F[B])(implicit F: FlatMap[F]): F[B] = F.flatMap(fa)(_ => fb)
 
   @deprecated("Use <* instead", "1.0.0-RC1")
   def <<[B](fb: F[B])(implicit F: FlatMap[F]): F[A] = F.forEffect(fa)(fb)