diff --git a/core/src/main/scala/cats/ApplicativeError.scala b/core/src/main/scala/cats/ApplicativeError.scala
index a64affd5cb6..ae71da6c3b5 100644
--- a/core/src/main/scala/cats/ApplicativeError.scala
+++ b/core/src/main/scala/cats/ApplicativeError.scala
@@ -2,6 +2,8 @@ package cats
 
 import cats.data.{EitherT, Validated}
 import cats.data.Validated.{Invalid, Valid}
+import cats.ApplicativeError.CatchOnlyPartiallyApplied
+import cats.data.EitherT
 
 import scala.reflect.ClassTag
 import scala.util.{Failure, Success, Try}
@@ -157,8 +159,6 @@ trait ApplicativeError[F[_], E] extends Applicative[F] {
    * @param fa is the source whose result is going to get transformed
    * @param recover is the function that gets called to recover the source
    *        in case of error
-   * @param map is the function that gets to transform the source
-   *        in case of success
    */
   def redeem[A, B](fa: F[A])(recover: E => B, f: A => B): F[B] =
     handleError(map(fa)(f))(recover)
@@ -216,6 +216,12 @@ trait ApplicativeError[F[_], E] extends Applicative[F] {
       case NonFatal(e) => raiseError(e)
     }
 
+  /**
+   * Evaluates the specified block, catching exceptions of the specified type. Uncaught exceptions are propagated.
+   */
+  def catchOnly[T >: Null <: Throwable]: CatchOnlyPartiallyApplied[T, F, E] =
+    new CatchOnlyPartiallyApplied[T, F, E](this)
+
   /**
    * If the error type is Throwable, we can convert from a scala.util.Try
    */
@@ -301,6 +307,17 @@ object ApplicativeError {
       }
   }
 
+  final private[cats] class CatchOnlyPartiallyApplied[T, F[_], E](private val F: ApplicativeError[F, E])
+      extends AnyVal {
+    def apply[A](f: => A)(implicit CT: ClassTag[T], NT: NotNull[T], ev: Throwable <:< E): F[A] =
+      try {
+        F.pure(f)
+      } catch {
+        case t if CT.runtimeClass.isInstance(t) =>
+          F.raiseError(t)
+      }
+  }
+
   /**
    * lift from scala.Option[A] to a F[A]
    *
diff --git a/core/src/main/scala/cats/instances/try.scala b/core/src/main/scala/cats/instances/try.scala
index b1b571b0066..3e98c024fe1 100644
--- a/core/src/main/scala/cats/instances/try.scala
+++ b/core/src/main/scala/cats/instances/try.scala
@@ -137,6 +137,10 @@ trait TryInstances extends TryInstances1 {
         }
 
       override def isEmpty[A](fa: Try[A]): Boolean = fa.isFailure
+
+      override def catchNonFatal[A](a: => A)(implicit ev: Throwable <:< Throwable): Try[A] = Try(a)
+
+      override def catchNonFatalEval[A](a: Eval[A])(implicit ev: Throwable <:< Throwable): Try[A] = Try(a.value)
     }
   // scalastyle:on method.length
 
diff --git a/tests/src/test/scala/cats/tests/TrySuite.scala b/tests/src/test/scala/cats/tests/TrySuite.scala
index f59ad050a70..ef3d698c55e 100644
--- a/tests/src/test/scala/cats/tests/TrySuite.scala
+++ b/tests/src/test/scala/cats/tests/TrySuite.scala
@@ -61,6 +61,17 @@ class TrySuite extends CatsSuite {
       res should not be (null)
     }
   }
+
+  test("catchOnly works") {
+    forAll { e: Either[String, Int] =>
+      val str = e.fold(identity, _.toString)
+      val res = MonadError[Try, Throwable].catchOnly[NumberFormatException](str.toInt)
+      // the above should just never cause an uncaught exception
+      // this is a somewhat bogus test:
+      res should not be (null)
+    }
+  }
+
   test("fromTry works") {
     forAll { t: Try[Int] =>
       (MonadError[Try, Throwable].fromTry(t)) should ===(t)