diff --git a/haystack/core/pipeline/base.py b/haystack/core/pipeline/base.py
index be7c0737d0..9a656552dd 100644
--- a/haystack/core/pipeline/base.py
+++ b/haystack/core/pipeline/base.py
@@ -916,13 +916,12 @@ def _distribute_output(
 
             is_greedy = getattr(receiver, "__haystack_is_greedy__", False)
             if receiver_socket.is_variadic and is_greedy:
-                # If the receiver is greedy, we can run it right away.
+                # If the receiver is greedy, we can run it as soon as possible.
                 # First we remove it from the status lists it's in if it's there or we risk running it multiple times.
-                if pair in to_run:
-                    to_run.remove(pair)
                 if pair in waiting_for_input:
                     waiting_for_input.remove(pair)
-                to_run.append(pair)
+                if pair not in to_run:
+                    to_run.append(pair)
 
             if pair not in waiting_for_input and pair not in to_run:
                 # Queue up the Component that received this input to run, only if it's not already waiting