diff --git a/var/spack/repos/builtin/packages/py-pyzmq/package.py b/var/spack/repos/builtin/packages/py-pyzmq/package.py
index 6aec08c715..e1031fb659 100644
--- a/var/spack/repos/builtin/packages/py-pyzmq/package.py
+++ b/var/spack/repos/builtin/packages/py-pyzmq/package.py
@@ -41,8 +41,6 @@ class PyPyzmq(PythonPackage):
     version("16.0.2", sha256="0322543fff5ab6f87d11a8a099c4c07dd8a1719040084b6ce9162bcdf5c45c9d")
     version("14.7.0", sha256="77994f80360488e7153e64e5959dc5471531d1648e3a4bff14a714d074a38cc2")
 
-    # Python 3.9 build issues
-    depends_on("python@2.7,3.3:3.8", type=("build", "run"), when="@16:18.0")
     depends_on("python@2.6:2.7,3.2:3.8", type=("build", "run"), when="@:14")
 
     # pyproject.toml
@@ -62,6 +60,15 @@ class PyPyzmq(PythonPackage):
     # Undocumented dependencies
     depends_on("py-gevent", type=("build", "run"))
 
+    @run_before("install")
+    @when("@15:19")
+    def remove_cythonized_files(self):
+        # Before v20.0.0 an ancient cythonize API was used, for which we cannot
+        # force re-cythonization. Re-cythonizing v14.x fails in general, so
+        # restrict to 15:19
+        for f in find(".", "*.pyx"):
+            touch(f)
+
     @run_before("install")
     def setup(self):
         """Create config file listing dependency information."""