diff --git a/core/src/main/scala/cats/instances/future.scala b/core/src/main/scala/cats/instances/future.scala
index 0518529ed0..65f81b84cb 100644
--- a/core/src/main/scala/cats/instances/future.scala
+++ b/core/src/main/scala/cats/instances/future.scala
@@ -1,8 +1,8 @@
 package cats
 package instances
 
-import scala.util.control.NonFatal
 import scala.concurrent.{ExecutionContext, Future}
+import scala.util.control.NonFatal
 
 trait FutureInstances extends FutureInstances1 {
 
@@ -10,28 +10,38 @@ trait FutureInstances extends FutureInstances1 {
     implicit ec: ExecutionContext
   ): MonadError[Future, Throwable] with CoflatMap[Future] with Monad[Future] =
     new FutureCoflatMap with MonadError[Future, Throwable] with Monad[Future] with StackSafeMonad[Future] {
-      def pure[A](x: A): Future[A] = Future.successful(x)
+      def pure[A](x: A): Future[A] =
+        Future.successful(x)
+
+      def flatMap[A, B](fa: Future[A])(f: A => Future[B]): Future[B] =
+        fa.flatMap(f)
 
-      def flatMap[A, B](fa: Future[A])(f: A => Future[B]): Future[B] = fa.flatMap(f)
+      def handleErrorWith[A](fea: Future[A])(f: Throwable => Future[A]): Future[A] =
+        fea.recoverWith { case t => f(t) }
 
-      def handleErrorWith[A](fea: Future[A])(f: Throwable => Future[A]): Future[A] = fea.recoverWith { case t => f(t) }
+      def raiseError[A](e: Throwable): Future[A] =
+        Future.failed(e)
 
-      def raiseError[A](e: Throwable): Future[A] = Future.failed(e)
-      override def handleError[A](fea: Future[A])(f: Throwable => A): Future[A] = fea.recover { case t => f(t) }
+      override def handleError[A](fea: Future[A])(f: Throwable => A): Future[A] =
+        fea.recover { case t => f(t) }
 
       override def attempt[A](fa: Future[A]): Future[Either[Throwable, A]] =
         (fa.map(a => Right[Throwable, A](a))).recover { case NonFatal(t) => Left(t) }
 
-      override def recover[A](fa: Future[A])(pf: PartialFunction[Throwable, A]): Future[A] = fa.recover(pf)
+      override def recover[A](fa: Future[A])(pf: PartialFunction[Throwable, A]): Future[A] =
+        fa.recover(pf)
 
       override def recoverWith[A](fa: Future[A])(pf: PartialFunction[Throwable, Future[A]]): Future[A] =
         fa.recoverWith(pf)
 
-      override def map[A, B](fa: Future[A])(f: A => B): Future[B] = fa.map(f)
+      override def map[A, B](fa: Future[A])(f: A => B): Future[B] =
+        fa.map(f)
 
-      override def catchNonFatal[A](a: => A)(implicit ev: Throwable <:< Throwable): Future[A] = Future(a)
+      override def catchNonFatal[A](a: => A)(implicit ev: Throwable <:< Throwable): Future[A] =
+        Future(a)
 
-      override def catchNonFatalEval[A](a: Eval[A])(implicit ev: Throwable <:< Throwable): Future[A] = Future(a.value)
+      override def catchNonFatalEval[A](a: Eval[A])(implicit ev: Throwable <:< Throwable): Future[A] =
+        Future(a.value)
     }
 }
 
diff --git a/core/src/main/scala/cats/instances/try.scala b/core/src/main/scala/cats/instances/try.scala
index 8816d47e3c..5ec80f0193 100644
--- a/core/src/main/scala/cats/instances/try.scala
+++ b/core/src/main/scala/cats/instances/try.scala
@@ -1,11 +1,10 @@
 package cats
 package instances
 
-import TryInstances.castFailure
+import cats.instances.TryInstances.castFailure
 
-import scala.util.control.NonFatal
-import scala.util.{Failure, Success, Try}
 import scala.annotation.tailrec
+import scala.util.{Failure, Success, Try}
 
 trait TryInstances extends TryInstances1 {
 
@@ -69,7 +68,7 @@ trait TryInstances extends TryInstances1 {
         ta.recover { case t => f(t) }
 
       override def attempt[A](ta: Try[A]): Try[Either[Throwable, A]] =
-        (ta.map(a => Right[Throwable, A](a))).recover { case NonFatal(t) => Left(t) }
+        ta match { case Success(a) => Success(Right(a)); case Failure(e) => Success(Left(e)) }
 
       override def recover[A](ta: Try[A])(pf: PartialFunction[Throwable, A]): Try[A] =
         ta.recover(pf)
diff --git a/core/src/main/scala/cats/syntax/applicativeError.scala b/core/src/main/scala/cats/syntax/applicativeError.scala
index 353d739b10..6657729c52 100644
--- a/core/src/main/scala/cats/syntax/applicativeError.scala
+++ b/core/src/main/scala/cats/syntax/applicativeError.scala
@@ -100,6 +100,35 @@ final class ApplicativeErrorOps[F[_], E, A](private val fa: F[A]) extends AnyVal
   def recoverWith(pf: PartialFunction[E, F[A]])(implicit F: ApplicativeError[F, E]): F[A] =
     F.recoverWith(fa)(pf)
 
+  /**
+   * Returns a new value that transforms the result of the source,
+   * given the `recover` or `map` functions, which get executed depending
+   * on whether the result is successful or if it ends in error.
+   *
+   * This is an optimization on usage of [[attempt]] and [[Functor.map]],
+   * this equivalence being available:
+   *
+   * {{{
+   *   fa.redeem(fe, fs) <-> fa.attempt.map(_.fold(fe, fs))
+   * }}}
+   *
+   * Usage of `redeem` subsumes [[handleError]] because:
+   *
+   * {{{
+   *   fa.redeem(fe, id) <-> fa.handleError(fe)
+   * }}}
+   *
+   *
+   * @see [[MonadErrorOps.redeemWith]], [[attempt]] and [[handleError]]
+   *
+   * @param recover is the function that gets called to recover the source
+   *        in case of error
+   * @param f is the function that gets to transform the source
+   *        in case of success
+   */
+  def redeem[B](recover: E => B, f: A => B)(implicit F: ApplicativeError[F, E]): F[B] =
+    F.handleError(F.map(fa)(f))(recover)
+
   def onError(pf: PartialFunction[E, F[Unit]])(implicit F: ApplicativeError[F, E]): F[A] =
     F.onError(fa)(pf)
 
diff --git a/core/src/main/scala/cats/syntax/monadError.scala b/core/src/main/scala/cats/syntax/monadError.scala
index f6964dfeb0..aac82880ff 100644
--- a/core/src/main/scala/cats/syntax/monadError.scala
+++ b/core/src/main/scala/cats/syntax/monadError.scala
@@ -29,6 +29,40 @@ final class MonadErrorOps[F[_], E, A](private val fa: F[A]) extends AnyVal {
 
   def adaptError(pf: PartialFunction[E, E])(implicit F: MonadError[F, E]): F[A] =
     F.adaptError(fa)(pf)
+
+  /**
+   * Returns a new value that transforms the result of the source,
+   * given the `recover` or `bind` functions, which get executed depending
+   * on whether the result is successful or if it ends in error.
+   *
+   * This is an optimization on usage of [[ApplicativeError.attempt]] and [[FlatMap.flatMap]],
+   * this equivalence being available:
+   *
+   * {{{
+   *   fa.redeemWith(fe, fs) <-> fa.attempt.flatMap(_.fold(fe, fs))
+   * }}}
+   *
+   * Usage of `redeemWith` subsumes [[ApplicativeError.handleErrorWith]] because:
+   *
+   * {{{
+   *   fa.redeemWith(fe, F.pure) <-> fa.handleErrorWith(fe)
+   * }}}
+   *
+   * Usage of `redeemWith` also subsumes [[FlatMap.flatMap]] because:
+   *
+   * {{{
+   *   fa.redeemWith(F.raiseError, fs) <-> fa.flatMap(fs)
+   * }}}
+   *
+   * @see [[ApplicativeErrorOps.redeem]], [[ApplicativeError.attempt]] and [[ApplicativeError.handleErrorWith]]
+   *
+   * @param recover is the function that gets called to recover the source
+   *        in case of error
+   * @param bind is the function that gets to transform the source
+   *        in case of success
+   */
+  def redeemWith[B](recover: E => F[B], bind: A => F[B])(implicit F: MonadError[F, E]): F[B] =
+    F.flatMap(F.attempt(fa))(_.fold(recover, bind))
 }
 
 final class MonadErrorRethrowOps[F[_], E, A](private val fea: F[Either[E, A]]) extends AnyVal {
diff --git a/tests/src/test/scala/cats/tests/SyntaxSuite.scala b/tests/src/test/scala/cats/tests/SyntaxSuite.scala
index 2752af4f14..39804cbc7d 100644
--- a/tests/src/test/scala/cats/tests/SyntaxSuite.scala
+++ b/tests/src/test/scala/cats/tests/SyntaxSuite.scala
@@ -381,7 +381,7 @@ object SyntaxSuite
     val done = a.tailRecM[F, B](a => returnValue)
   }
 
-  def testApplicativeError[F[_, _], E, A](implicit F: ApplicativeError[F[E, *], E]): Unit = {
+  def testApplicativeError[F[_, _], E, A, B](implicit F: ApplicativeError[F[E, *], E]): Unit = {
     type G[X] = F[E, X]
 
     val e = mock[E]
@@ -404,12 +404,49 @@ object SyntaxSuite
 
     val pfegea = mock[PartialFunction[E, G[A]]]
     val gea4 = ga.recoverWith(pfegea)
+
+    val eb = mock[E => B]
+    val ab = mock[A => B]
+    val gb: G[B] = gea.redeem(eb, ab)
   }
 
   def testApplicativeErrorSubtype[F[_], A](implicit F: ApplicativeError[F, CharSequence]): Unit = {
     val fea = "meow".raiseError[F, A]
   }
 
+  def testMonadError[F[_, _], E, A, B](implicit F: MonadError[F[E, *], E]): Unit = {
+    type G[X] = F[E, X]
+
+    val e = mock[E]
+    val ga = e.raiseError[G, A]
+
+    val gea = mock[G[A]]
+
+    val ea = mock[E => A]
+    val gea1 = ga.handleError(ea)
+
+    val egea = mock[E => G[A]]
+    val gea2 = ga.handleErrorWith(egea)
+
+    val gxea = ga.attempt
+
+    val gxtea = ga.attemptT
+
+    val pfea = mock[PartialFunction[E, A]]
+    val gea3 = ga.recover(pfea)
+
+    val pfegea = mock[PartialFunction[E, G[A]]]
+    val gea4 = ga.recoverWith(pfegea)
+
+    val eb = mock[E => B]
+    val ab = mock[A => B]
+    val gb: G[B] = gea.redeem(eb, ab)
+
+    val efb = mock[E => G[B]]
+    val afb = mock[A => G[B]]
+    val gb2: G[B] = gea.redeemWith(efb, afb)
+  }
+
   def testNested[F[_], G[_], A]: Unit = {
     val fga: F[G[A]] = mock[F[G[A]]]