diff --git a/python-zmq.spec b/python-zmq.spec
index 3aa099b..77d8710 100644
--- a/python-zmq.spec
+++ b/python-zmq.spec
@@ -76,7 +76,6 @@ messaging implementation.}
 
 %package -n python%{python3_pkgversion}-zmq
 Summary:        %{summary}
-License:        LGPLv3+
 %py_provides    python%{python3_pkgversion}-pyzmq
 
 %description -n python%{python3_pkgversion}-zmq %{common_description}
@@ -84,7 +83,10 @@ License:        LGPLv3+
 
 %package -n python%{python3_pkgversion}-zmq-tests
 Summary:        %{summary}, testsuite
-License:        LGPLv3+
+# This subpackage does not contain any of the files that are under other
+# licenses; see the comment above the main License tag.
+License:        BSD-3-Clause
+
 Requires:       python%{python3_pkgversion}-zmq = %{version}-%{release}
 %py_provides    python%{python3_pkgversion}-pyzmq-tests