diff --git a/lib/spack/spack/spec.py b/lib/spack/spack/spec.py
index 69fb895bf51..36ea507bd61 100644
--- a/lib/spack/spack/spec.py
+++ b/lib/spack/spack/spec.py
@@ -1817,7 +1817,9 @@ def _add_dependency(
             )
         except StopIteration:
             # Error if we have overlapping or incompatible deptypes
-            if any(not dt.compatible(dspec.depflag, depflag) for dspec in orig):
+            if any(not dt.compatible(dspec.depflag, depflag) for dspec in orig) and all(
+                dspec.when == when for dspec in orig
+            ):
                 edge_attrs = f"deptypes={dt.flag_to_chars(depflag).strip()}"
                 required_dep_str = f"^[{edge_attrs}] {str(spec)}"
 
@@ -3440,7 +3442,11 @@ def satisfies(self, other: Union[str, "Spec"], deps: bool = True) -> bool:
         mock_nodes_from_old_specfiles = set()
         for rhs_edge in other.traverse_edges(root=False, cover="edges"):
             # Skip checking any conditional edge that is not satisfied
-            if rhs_edge.when != Spec() and not rhs_edge.parent.satisfies(rhs_edge.when):
+            if (
+                rhs_edge.when != Spec()
+                and not rhs_edge.parent.satisfies(rhs_edge.when)
+                and not self.satisfies(rhs_edge.when)
+            ):
                 continue
 
             # If we are checking for ^mpi we need to verify if there is any edge
@@ -3527,13 +3533,17 @@ def satisfies(self, other: Union[str, "Spec"], deps: bool = True) -> bool:
         for rhs in other.traverse(root=False):
             # Possible lhs nodes to match this rhs node
             lhss = [lhs for lhs in lhs_nodes if lhs.satisfies(rhs, deps=False)]
+            lhs_parents = [
+                lhs
+                for lhs in lhs_nodes
+                if any(lhs.satisfies(parent, deps=False) for parent in rhs.dependents())
+            ]
 
             # Check whether the node needs matching (not a conditional that isn't satisfied)
             in_edges = [
                 e
                 for e in rhs.edges_from_dependents()
-                if e.parent.satisfies(e.when)
-                or (lhss and all(lhs.satisfies(e.when) for lhs in lhss))
+                if e.parent.satisfies(e.when) or any(lhp.satisfies(e.when) for lhp in lhs_parents)
             ]
             if not in_edges:
                 continue
@@ -3676,6 +3686,7 @@ def spid(spec):
                 depflag=edge.depflag,
                 virtuals=edge.virtuals,
                 direct=edge.direct,
+                when=edge.when,
             )
 
     def copy(self, deps: Union[bool, dt.DepTypes, dt.DepFlag] = True, **kwargs):
diff --git a/lib/spack/spack/test/spec_semantics.py b/lib/spack/spack/test/spec_semantics.py
index 70bbb7fb078..8a0f977a11c 100644
--- a/lib/spack/spack/test/spec_semantics.py
+++ b/lib/spack/spack/test/spec_semantics.py
@@ -327,6 +327,26 @@ class TestSpecSemantics:
                     "ba5e334fe247335f3a116decfb5284100791dc302b5571ff5e664d8f9a6806c2"
                 ),
             ),
+            (
+                "libelf",
+                "%[when='^c' virtuals=c]gcc ^[when='+mpi' virtuals=mpi]mpich",
+                "libelf %[when='^c' virtuals=c]gcc ^[when='+mpi' virtuals=mpi]mpich",
+            ),
+            (
+                "libelf %[when='^c' virtuals=c]gcc",
+                "%[when='^c' virtuals=c]gcc@10.3.1",
+                "libelf%[when='^c' virtuals=c]gcc@10.3.1",
+            ),
+            (
+                "libelf %[when='^c' virtuals=c]gcc",
+                "%[when='^c' virtuals=c]gcc@10.3.1 ^[when='+mpi'] mpich",
+                "libelf%[when='^c' virtuals=c]gcc@10.3.1 ^[when='+mpi']mpich",
+            ),
+            (
+                "libelf %[when='^c' virtuals=c]gcc",
+                "%[when='^cxx' virtuals=cxx]gcc@10.3.1",
+                "libelf%[when='^c' virtuals=c]gcc %[when='^cxx' virtuals=cxx]gcc@10.3.1",
+            ),
         ],
     )
     def test_abstract_specs_can_constrain_each_other(self, lhs, rhs, expected):
@@ -573,6 +593,14 @@ def test_abstract_specs_with_propagation(self, lhs, rhs, expected, constrained):
         c.constrain(lhs)
         assert c == constrained
 
+    def test_satisfies_conditional_dep(self):
+        concrete = spack.concretize.concretize_one("mpileaks^mpich")
+        assert concrete.satisfies("^[when='^mpi' virtuals=mpi]mpich")
+        assert concrete.satisfies("^[when='^notapackage']zmpi")
+        assert not concrete.satisfies("^[virtuals=blas]mpich")
+        assert not concrete.satisfies("^[when='^mpi' virtuals=blas]mpich")
+        assert not concrete.satisfies("^[when='^mpi']zmpi")
+
     def test_satisfies_single_valued_variant(self):
         """Tests that the case reported in
         https://github.com/spack/spack/pull/2386#issuecomment-282147639