diff --git a/lib/spack/spack/build_environment.py b/lib/spack/spack/build_environment.py
index 9908ad9834d..d38617628bd 100644
--- a/lib/spack/spack/build_environment.py
+++ b/lib/spack/spack/build_environment.py
@@ -923,7 +923,9 @@ def effective_deptypes(
     in reverse so that dependents override dependencies, not the other way around."""
     topo_sorted_edges = traverse.traverse_topo_edges_generator(
         traverse.with_artificial_edges(specs),
-        visitor=EnvironmentVisitor(*specs, context=context),
+        visitor=traverse.CoverEdgesVisitor(
+            EnvironmentVisitor(*specs, context=context), key=traverse.by_dag_hash
+        ),
         key=traverse.by_dag_hash,
         root=True,
         all_edges=True,
diff --git a/lib/spack/spack/traverse.py b/lib/spack/spack/traverse.py
index e143a214543..d9f76072025 100644
--- a/lib/spack/spack/traverse.py
+++ b/lib/spack/spack/traverse.py
@@ -381,7 +381,7 @@ def traverse_topo_edges_generator(edges, visitor, key=id, root=True, all_edges=F
 
     Arguments:
         edges (list): List of EdgeAndDepth instances
-        visitor: visitor instance that defines the sub-DAG to traverse
+        visitor: visitor that produces unique edges defining the (sub)DAG of interest.
         key: function that takes a spec and outputs a key for uniqueness test.
         root (bool): Yield the root nodes themselves
         all_edges (bool): When ``False`` only one in-edge per node is returned, when