diff --git a/sdks/go/pkg/beam/runners/prism/internal/coders.go b/sdks/go/pkg/beam/runners/prism/internal/coders.go
index ffea90e79065..6b88790521ce 100644
--- a/sdks/go/pkg/beam/runners/prism/internal/coders.go
+++ b/sdks/go/pkg/beam/runners/prism/internal/coders.go
@@ -35,6 +35,11 @@ import (
 // leafCoders lists coder urns the runner knows how to manipulate.
 // In particular, ones that won't be a problem to parse, in general
 // because they have a known total size.
+//
+// Important: The 'leafCoders' and 'knownCompositeCoders' do not necessarily
+// cover all possible standard coder types.
+// For example, coderRow is neither a leaf coder nor a composite coder (so it
+// will have to be LP'd).
 var leafCoders = map[string]struct{}{
 	urns.CoderBytes:          {},
 	urns.CoderStringUTF8:     {},
@@ -51,6 +56,28 @@ func isLeafCoder(c *pipepb.Coder) bool {
 	return ok
 }
 
+// knownCompositeCoders lists coder urns that we expect to see components in
+// their spec.
+var knownCompositeCoders = map[string]struct{}{
+	urns.CoderKV:                  {},
+	urns.CoderIterable:            {},
+	urns.CoderTimer:               {},
+	urns.CoderWindowedValue:       {},
+	urns.CoderParamWindowedValue:  {},
+	urns.CoderStateBackedIterable: {},
+	urns.CoderCustomWindow:        {},
+	urns.CoderShardedKey:          {},
+	urns.CoderNullable:            {},
+	// Exclude CoderLengthPrefix from the list. Even though it is a composite coder,
+	// we never need to introspect its component.
+	// urns.CoderLengthPrefix:     {},
+}
+
+func isKnownCompositeCoder(c *pipepb.Coder) bool {
+	_, ok := knownCompositeCoders[c.GetSpec().GetUrn()]
+	return ok
+}
+
 // makeWindowedValueCoder gets the coder for the PCollection, renders it safe, and adds it to the coders map.
 //
 // PCollection coders are not inherently WindowValueCoder wrapped, and they are added by the runner
@@ -123,10 +150,10 @@ func lpUnknownCoders(cID string, bundle, base map[string]*pipepb.Coder) (string,
 	}
 	// Add the original coder to the coders map.
 	bundle[cID] = c
-	// If we don't know this coder, and it has no sub components,
-	// we must LP it, and we return the LP'd version.
+	// If we don't know this coder, we must LP it, and we return the LP'd version.
 	leaf := isLeafCoder(c)
-	if len(c.GetComponentCoderIds()) == 0 && !leaf {
+	knownComposite := isKnownCompositeCoder(c)
+	if !leaf && !knownComposite {
 		lpc := &pipepb.Coder{
 			Spec: &pipepb.FunctionSpec{
 				Urn: urns.CoderLengthPrefix,
@@ -136,8 +163,7 @@ func lpUnknownCoders(cID string, bundle, base map[string]*pipepb.Coder) (string,
 		bundle[lpcID] = lpc
 		return lpcID, nil
 	}
-	// We know we have a composite, so if we count this as a leaf, move everything to
-	// the coders map.
+	// If it is a leaf, move its components (if any) to the coders map.
 	if leaf {
 		// Copy the components from the base.
 		for _, cc := range c.GetComponentCoderIds() {
@@ -145,6 +171,10 @@ func lpUnknownCoders(cID string, bundle, base map[string]*pipepb.Coder) (string,
 		}
 		return cID, nil
 	}
+
+	// Now we have a known composite.
+	// We may need to LP its components. If so, we make a new composite with the
+	// LP'd components.
 	var needNewComposite bool
 	var comps []string
 	for i, cc := range c.GetComponentCoderIds() {
diff --git a/sdks/python/apache_beam/runners/portability/prism_runner_test.py b/sdks/python/apache_beam/runners/portability/prism_runner_test.py
index 57bd78be3068..0a08ec7d358d 100644
--- a/sdks/python/apache_beam/runners/portability/prism_runner_test.py
+++ b/sdks/python/apache_beam/runners/portability/prism_runner_test.py
@@ -217,11 +217,6 @@ def test_custom_window_type(self):
         "Requires Prism to support Custom Window Coders." +
         " https://github.com/apache/beam/issues/31921")
 
-  def test_pack_combiners(self):
-    raise unittest.SkipTest(
-        "Requires Prism to support coder:" +
-        " 'beam:coder:tuple:v1'. https://github.com/apache/beam/issues/32636")
-
   def test_metrics(self):
     super().test_metrics(check_bounded_trie=False)