diff --git a/core/src/main/scala/cats/data/EitherT.scala b/core/src/main/scala/cats/data/EitherT.scala
index a267f9684c..61e462ca40 100644
--- a/core/src/main/scala/cats/data/EitherT.scala
+++ b/core/src/main/scala/cats/data/EitherT.scala
@@ -49,7 +49,7 @@ final case class EitherT[F[_], A, B](value: F[Either[A, B]]) {
   /**
    * Inverse of `MonadError#attemptT`
    */
-  def rethrowT(implicit F: MonadError[F, A]): F[B] =
+  def rethrowT(implicit F: MonadError[F, _ >: A]): F[B] =
     F.rethrow(value)
 
   def valueOr[BB >: B](f: A => BB)(implicit F: Functor[F]): F[BB] = fold(f, identity)
diff --git a/core/src/main/scala/cats/syntax/either.scala b/core/src/main/scala/cats/syntax/either.scala
index bca66e12db..c63cf5268c 100644
--- a/core/src/main/scala/cats/syntax/either.scala
+++ b/core/src/main/scala/cats/syntax/either.scala
@@ -276,6 +276,7 @@ final class EitherOps[A, B](private val eab: Either[A, B]) extends AnyVal {
 
   def toEitherNel[AA >: A]: EitherNel[AA, B] = leftMap(NonEmptyList.one)
 
+  @deprecated("use liftTo instead", "2.0.0")
   def raiseOrPure[F[_]](implicit ev: ApplicativeError[F, A]): F[B] =
     ev.fromEither(eab)
 
diff --git a/core/src/main/scala/cats/syntax/validated.scala b/core/src/main/scala/cats/syntax/validated.scala
index 6e76c52cf3..547011cf60 100644
--- a/core/src/main/scala/cats/syntax/validated.scala
+++ b/core/src/main/scala/cats/syntax/validated.scala
@@ -20,7 +20,7 @@ trait ValidatedExtensionSyntax {
 }
 
 final class ValidatedExtension[E, A](private val self: Validated[E, A]) extends AnyVal {
-  def liftTo[F[_]](implicit F: ApplicativeError[F, E]): F[A] =
+  def liftTo[F[_]](implicit F: ApplicativeError[F, _ >: E]): F[A] =
     new ApplicativeErrorExtensionOps(F).fromValidated(self)
 }
 
diff --git a/tests/src/test/scala/cats/tests/EitherTSuite.scala b/tests/src/test/scala/cats/tests/EitherTSuite.scala
index 0e637b2859..ce9886058b 100644
--- a/tests/src/test/scala/cats/tests/EitherTSuite.scala
+++ b/tests/src/test/scala/cats/tests/EitherTSuite.scala
@@ -285,6 +285,15 @@ class EitherTSuite extends CatsSuite {
     failed.attemptT.rethrowT should ===(failed)
   }
 
+  test("rethrowT works with specialized failures") {
+    implicit val eqThrow: Eq[Throwable] = Eq.fromUniversalEquals
+    val failed: Try[Int] = Failure(new IllegalArgumentException("error"))
+
+    val t: EitherT[Try, IllegalArgumentException, Int] =
+      failed.attemptT.leftMap(_.asInstanceOf[IllegalArgumentException])
+    t.rethrowT should ===(failed)
+  }
+
   test("transform consistent with value.map") {
     forAll { (eithert: EitherT[List, String, Int], f: Either[String, Int] => Either[Long, Double]) =>
       eithert.transform(f) should ===(EitherT(eithert.value.map(f)))
diff --git a/tests/src/test/scala/cats/tests/ValidatedSuite.scala b/tests/src/test/scala/cats/tests/ValidatedSuite.scala
index faf6fb70fe..a7bc31cb29 100644
--- a/tests/src/test/scala/cats/tests/ValidatedSuite.scala
+++ b/tests/src/test/scala/cats/tests/ValidatedSuite.scala
@@ -314,4 +314,13 @@ class ValidatedSuite extends CatsSuite {
       v.liftTo[Option] shouldBe v.toOption
     }
   }
+
+  test("liftTo works with specialized errors") {
+    implicit val eqThrow: Eq[Throwable] = Eq.fromUniversalEquals
+    val ex: IllegalArgumentException = new IllegalArgumentException()
+    val validated: Validated[IllegalArgumentException, Int] = Validated.Invalid(ex)
+    val lifted: Either[Throwable, Int] = validated.liftTo[Either[Throwable, *]]
+
+    lifted should ===(Left[Throwable, Int](ex))
+  }
 }