diff --git a/src/pip/_internal/cli/req_command.py b/src/pip/_internal/cli/req_command.py
index 104b033281f..deb105cac27 100644
--- a/src/pip/_internal/cli/req_command.py
+++ b/src/pip/_internal/cli/req_command.py
@@ -314,7 +314,7 @@ def get_requirements(
                     parsed_req,
                     isolated=options.isolated_mode,
                 )
-                req_to_add.is_direct = True
+                req_to_add.is_direct = False
                 requirement_set.add_requirement(req_to_add)
 
         for req in args:
diff --git a/src/pip/_internal/req/req_set.py b/src/pip/_internal/req/req_set.py
index f168ce17abd..7d6ad182eec 100644
--- a/src/pip/_internal/req/req_set.py
+++ b/src/pip/_internal/req/req_set.py
@@ -110,9 +110,8 @@ def add_requirement(
                 )
 
         # This next bit is really a sanity check.
-        assert install_req.is_direct == (parent_req_name is None), (
-            "a direct req shouldn't have a parent and also, "
-            "a non direct req should have a parent"
+        assert not install_req.is_direct or parent_req_name is None, (
+            "a direct req shouldn't have a parent"
         )
 
         # Unnamed requirements are scanned again and the requirement won't be
@@ -167,6 +166,10 @@ def add_requirement(
         # If we're now installing a constraint, mark the existing
         # object for real installation.
         existing_req.constraint = False
+        # If we're now installing a top level requirement, mark the existing
+        # object as top level.
+        if install_req.is_direct:
+            existing_req.is_direct = True
         existing_req.extras = tuple(sorted(
             set(existing_req.extras) | set(install_req.extras)
         ))
diff --git a/src/pip/_internal/resolution/legacy/resolver.py b/src/pip/_internal/resolution/legacy/resolver.py
index cdb44d19dbe..977cb6a57f8 100644
--- a/src/pip/_internal/resolution/legacy/resolver.py
+++ b/src/pip/_internal/resolution/legacy/resolver.py
@@ -194,7 +194,7 @@ def _is_upgrade_allowed(self, req):
             return True
         else:
             assert self.upgrade_strategy == "only-if-needed"
-            return req.is_direct
+            return req.is_direct or req.constraint
 
     def _set_req_to_reinstall(self, req):
         # type: (InstallRequirement) -> None