diff --git a/kernel/shared/src/main/scala/cats/effect/kernel/GenSpawn.scala b/kernel/shared/src/main/scala/cats/effect/kernel/GenSpawn.scala
index b678561ce4..0fe82eddff 100644
--- a/kernel/shared/src/main/scala/cats/effect/kernel/GenSpawn.scala
+++ b/kernel/shared/src/main/scala/cats/effect/kernel/GenSpawn.scala
@@ -300,6 +300,37 @@ trait GenSpawn[F[_], E] extends MonadCancel[F, E] with Unique[F] {
   def racePair[A, B](fa: F[A], fb: F[B])
       : F[Either[(Outcome[F, E, A], Fiber[F, E, B]), (Fiber[F, E, A], Outcome[F, E, B])]]
 
+  /**
+   * Races the evaluation of two fibers, cancels the loser, and returns the [[Outcome]] of both.
+   * If the race is canceled before one or both participants complete, then then whichever ones
+   * are incomplete are canceled.
+   *
+   * @param fa
+   *   the effect for the first racing fiber
+   * @param fb
+   *   the effect for the second racing fiber
+   */
+  def raceOutcomeBoth[A, B](fa: F[A], fb: F[B])
+      : F[Either[(Outcome[F, E, A], Outcome[F, E, B]), (Outcome[F, E, A], Outcome[F, E, B])]] =
+    uncancelable { poll =>
+      poll(racePair(fa, fb)).flatMap {
+        case Left((oca, f)) =>
+          val joined =
+            if (oca.isCanceled)
+              poll(f.join)
+            else
+              f.cancel *> f.join
+          joined.map(ocb => Left((oca, ocb)))
+        case Right((f, ocb)) =>
+          val joined =
+            if (ocb.isCanceled)
+              poll(f.join)
+            else
+              f.cancel *> f.join
+          joined.map(oca => Right((oca, ocb)))
+      }
+    }
+
   /**
    * Races the evaluation of two fibers that returns the [[Outcome]] of the winner. The winner
    * of the race is considered to be the first fiber that completes with an outcome. The loser
@@ -314,11 +345,9 @@ trait GenSpawn[F[_], E] extends MonadCancel[F, E] with Unique[F] {
    *   [[race]] for a simpler variant that returns the successful outcome.
    */
   def raceOutcome[A, B](fa: F[A], fb: F[B]): F[Either[Outcome[F, E, A], Outcome[F, E, B]]] =
-    uncancelable { poll =>
-      poll(racePair(fa, fb)).flatMap {
-        case Left((oc, f)) => f.cancel.as(Left(oc))
-        case Right((f, oc)) => f.cancel.as(Right(oc))
-      }
+    raceOutcomeBoth(fa, fb).map {
+      case Left((oc, _)) => Left(oc)
+      case Right((_, oc)) => Right(oc)
     }
 
   /**
@@ -345,33 +374,58 @@ trait GenSpawn[F[_], E] extends MonadCancel[F, E] with Unique[F] {
    *   [[raceOutcome]] for a variant that returns the outcome of the winner.
    */
   def race[A, B](fa: F[A], fb: F[B]): F[Either[A, B]] =
-    uncancelable { poll =>
-      poll(racePair(fa, fb)).flatMap {
-        case Left((oc, f)) =>
-          oc match {
-            case Outcome.Succeeded(fa) => f.cancel *> fa.map(Left(_))
-            case Outcome.Errored(ea) => f.cancel *> raiseError(ea)
-            case Outcome.Canceled() =>
-              poll(f.join).onCancel(f.cancel).flatMap {
-                case Outcome.Succeeded(fb) => fb.map(Right(_))
-                case Outcome.Errored(eb) => raiseError(eb)
-                case Outcome.Canceled() => poll(canceled) *> never
-              }
-          }
-        case Right((f, oc)) =>
-          oc match {
-            case Outcome.Succeeded(fb) => f.cancel *> fb.map(Right(_))
-            case Outcome.Errored(eb) => f.cancel *> raiseError(eb)
-            case Outcome.Canceled() =>
-              poll(f.join).onCancel(f.cancel).flatMap {
-                case Outcome.Succeeded(fa) => fa.map(Left(_))
-                case Outcome.Errored(ea) => raiseError(ea)
-                case Outcome.Canceled() => poll(canceled) *> never
-              }
-          }
+    raceOutcomeBoth(fa, fb).flatMap(embedRaceOutcome(_))
+
+  /**
+   * Like [[race]], but in the case that neither fiber completes with [[Outcome.Canceled]],
+   * priority is given to the outcome of the second fiber. Hence, this method is right-biased.
+   *
+   * @param fa
+   *   the effect for the first racing fiber
+   * @param fb
+   *   the effect for the second racing fiber
+   *
+   * @see
+   *   [[race]] for a non-biased variant
+   */
+  def raceBiased[A, B](fa: F[A], fb: F[B]): F[Either[A, B]] =
+    raceOutcomeBoth(fa, fb).flatMap { raceOutcome =>
+      raceOutcome.merge._2 match {
+        case Outcome.Succeeded(fb) => fb.map(Right(_))
+        case Outcome.Errored(eb) => raiseError(eb)
+        case Outcome.Canceled() => embedRaceOutcome(raceOutcome)
       }
     }
 
+  private[this] def embedRaceOutcome[A, B](
+      raceOutcome: Either[
+        (Outcome[F, E, A], Outcome[F, E, B]),
+        (Outcome[F, E, A], Outcome[F, E, B])]): F[Either[A, B]] =
+    raceOutcome match {
+      case Left((oca, ocb)) =>
+        oca match {
+          case Outcome.Succeeded(fa) => fa.map(Left(_))
+          case Outcome.Errored(ea) => raiseError(ea)
+          case Outcome.Canceled() =>
+            ocb match {
+              case Outcome.Succeeded(fb) => fb.map(Right(_))
+              case Outcome.Errored(eb) => raiseError(eb)
+              case Outcome.Canceled() => canceled *> never
+            }
+        }
+      case Right((oca, ocb)) =>
+        ocb match {
+          case Outcome.Succeeded(fb) => fb.map(Right(_))
+          case Outcome.Errored(eb) => raiseError(eb)
+          case Outcome.Canceled() =>
+            oca match {
+              case Outcome.Succeeded(fa) => fa.map(Left(_))
+              case Outcome.Errored(ea) => raiseError(ea)
+              case Outcome.Canceled() => canceled *> never
+            }
+        }
+    }
+
   /**
    * Races the evaluation of two fibers and returns the [[Outcome]] of both. If the race is
    * canceled before one or both participants complete, then then whichever ones are incomplete