diff --git a/core/shared/src/main/scala/fs2/Pull.scala b/core/shared/src/main/scala/fs2/Pull.scala
index 2ea73a9dce..f542280408 100644
--- a/core/shared/src/main/scala/fs2/Pull.scala
+++ b/core/shared/src/main/scala/fs2/Pull.scala
@@ -669,26 +669,24 @@ object Pull extends PullLowPriority {
       val del: Bind[F, O, Y, Unit]
   ) extends Bind[F, O, X, Unit](step) {
     def cont(tx: Terminal[X]): Pull[F, O, Unit] =
-      try bindBindAux(this, tx)
+      try bindBindAux(bb.cont(tx), del)
       catch { case NonFatal(e) => Fail(e) }
   }
 
   @tailrec @nowarn("cat=unchecked")
   private def bindBindAux[F[_], O, X, Y](
-      bibi: BindBind[F, O, X, Y],
-      tx: Terminal[X]
-  ): Pull[F, O, Unit] = {
-    val py: Pull[F, O, Y] = bibi.bb.cont(tx)
+      py: Pull[F, O, Y],
+      del: Bind[F, O, Y, Unit]
+  ): Pull[F, O, Unit] =
     py match {
       case ty: Terminal[_] =>
-        bibi.del match {
+        del match {
           case cici: BindBind[F, O, r, Y] =>
-            bindBindAux[F, O, r, Y](cici, ty)
-          case _ => bibi.del.cont(ty)
+            bindBindAux[F, O, r, Y](cici.bb.cont(ty), cici.del)
+          case _ => del.cont(ty)
         }
-      case x => new DelegateBind(x, bibi.del)
+      case x => new DelegateBind(x, del)
     }
-  }
 
   /* An action is an instruction that can perform effects in `F`
    * to generate by-product outputs of type `O`.
@@ -805,7 +803,7 @@ object Pull extends PullLowPriority {
   ): Pull[F, INothing, Option[(Chunk[O], Pull[F, O, Unit])]] =
     Uncons(s)
 
-  private type Cont[-Y, +G[_], +X] = Terminal[Y] => Pull[G, X, Unit]
+  private type Cont[-Y, +G[_], +O] = Terminal[Y] => Pull[G, O, Unit]
 
   private[this] type Nought[A] = Any
 
@@ -871,25 +869,28 @@ object Pull extends PullLowPriority {
 
       }
 
-    trait Run[G[_], X, End] {
+    trait Run[-G[_], -X, +End] {
       def done(scope: Scope[F]): End
       def out(head: Chunk[X], scope: Scope[F], tail: Pull[G, X, Unit]): End
       def interrupted(inter: Interrupted): End
       def fail(e: Throwable): End
     }
-    type CallRun[G[_], X, End] = Run[G, X, End] => End
+    type CallRun[+G[_], +X, End] = Run[G, X, End] => End
 
-    class BuildR[G[_], X, End] extends Run[G, X, F[CallRun[G, X, F[End]]]] {
+    object TheBuildR extends Run[Pure, INothing, F[CallRun[Pure, Nothing, F[INothing]]]] {
+      type TheRun = Run[Pure, INothing, F[INothing]]
       def fail(e: Throwable) = F.raiseError(e)
-
       def done(scope: Scope[F]) =
-        F.pure((cont: Run[G, X, F[End]]) => cont.done(scope))
-      def out(head: Chunk[X], scope: Scope[F], tail: Pull[G, X, Unit]) =
-        F.pure((cont: Run[G, X, F[End]]) => cont.out(head, scope, tail))
+        F.pure((cont: TheRun) => cont.done(scope))
+      def out(head: Chunk[INothing], scope: Scope[F], tail: Pull[Pure, INothing, Unit]) =
+        F.pure((cont: TheRun) => cont.out(head, scope, tail))
       def interrupted(i: Interrupted) =
-        F.pure((cont: Run[G, X, F[End]]) => cont.interrupted(i))
+        F.pure((cont: TheRun) => cont.interrupted(i))
     }
 
+    def buildR[G[_], X, End]: Run[G, X, F[CallRun[G, X, F[End]]]] =
+      TheBuildR.asInstanceOf[Run[G, X, F[CallRun[G, X, F[End]]]]]
+
     def go[G[_], X, End](
         scope: Scope[F],
         extendedTopLevelScope: Option[Scope[F]],
@@ -1184,13 +1185,13 @@ object Pull extends PullLowPriority {
         case u: Uncons[G, y] @unchecked =>
           val v = getCont[Option[(Chunk[y], Pull[G, y, Unit])], G, X]
           // a Uncons is run on the same scope, without shifting.
-          val runr = new BuildR[G, y, End]
+          val runr = buildR[G, y, End]
           F.unit >> go(scope, extendedTopLevelScope, translation, runr, u.stream).attempt
             .flatMap(_.fold(goErr(_, v), _.apply(new UnconsRunR(v))))
 
         case s: StepLeg[G, y] @unchecked =>
           val v = getCont[Option[Stream.StepLeg[G, y]], G, X]
-          val runr = new BuildR[G, y, End]
+          val runr = buildR[G, y, End]
           scope
             .shiftScope(s.scope, s.toString)
             .flatMap(go(_, extendedTopLevelScope, translation, runr, s.stream).attempt)