diff --git a/python-rpm-generators.spec b/python-rpm-generators.spec
index 2af6e6d..ea6fb97 100644
--- a/python-rpm-generators.spec
+++ b/python-rpm-generators.spec
@@ -5,7 +5,7 @@
 Name:           python-rpm-generators
 Summary:        Dependency generators for Python RPMs
 Version:        10
-Release:        2%{?dist}
+Release:        3%{?dist}
 
 # Originally all those files were part of RPM, so license is kept here
 License:        GPLv2+
@@ -49,6 +49,9 @@ install -Dpm0755 -t %{buildroot}%{_rpmconfigdir} pythondeps.sh pythondistdeps.py
 %{_rpmconfigdir}/pythondistdeps.py
 
 %changelog
+* Fri Jan 17 2020 Miro Hrončok <mhroncok@redhat.com> - 10-3
+- Also provide pythonXdist() with PEP 503 normalized names (#1791530)
+
 * Fri Jan 03 2020 Miro Hrončok <mhroncok@redhat.com> - 10-2
 - Fix more complicated requirement expressions by adding parenthesis
 
diff --git a/pythondistdeps.py b/pythondistdeps.py
index da5f1a0..8756fdf 100755
--- a/pythondistdeps.py
+++ b/pythondistdeps.py
@@ -32,6 +32,11 @@ PyMajorVer_Deps = False
 legacy_Provides = False
 legacy = False
 
+def normalize_name(name):
+    """https://www.python.org/dev/peps/pep-0503/#normalized-names"""
+    import re
+    return re.sub(r'[-_.]+', '-', name).lower()
+
 for o, a in opts:
     if o in ('-h', '--help'):
         print('-h, --help\tPrint help')
@@ -127,6 +132,12 @@ for f in files:
         import platform
         platform.python_version = lambda: dist.py_version
 
+        # This is the PEP 503 normalized name.
+        # It does also convert dots to dashes, unlike dist.key.
+        # In the current code, we only add additional provides with this.
+        # Later, we can start requiring them.
+        # See https://bugzilla.redhat.com/show_bug.cgi?id=1791530
+        normalized_name = normalize_name(dist.project_name)
 
         if Provides_PyMajorVer_Variant or PyMajorVer_Deps or legacy_Provides or legacy:
             # Get the Python major version
@@ -142,10 +153,16 @@ for f in files:
                 name = 'python{}dist({})'.format(dist.py_version, dist.key)
                 if name not in py_deps:
                     py_deps[name] = []
+                name_ = 'python{}dist({})'.format(dist.py_version, normalized_name)
+                if name_ not in py_deps:
+                    py_deps[name_] = []
             if Provides_PyMajorVer_Variant or PyMajorVer_Deps:
                 pymajor_name = 'python{}dist({})'.format(pyver_major, dist.key)
                 if pymajor_name not in py_deps:
                     py_deps[pymajor_name] = []
+                pymajor_name_ = 'python{}dist({})'.format(pyver_major, normalized_name)
+                if pymajor_name_ not in py_deps:
+                    py_deps[pymajor_name_] = []
             if legacy or legacy_Provides:
                 legacy_name = 'pythonegg({})({})'.format(pyver_major, dist.key)
                 if legacy_name not in py_deps:
@@ -158,8 +175,12 @@ for f in files:
                 if spec not in py_deps[name]:
                     if not legacy:
                         py_deps[name].append(spec)
+                        if name != name_:
+                            py_deps[name_].append(spec)
                     if Provides_PyMajorVer_Variant:
                         py_deps[pymajor_name].append(spec)
+                        if pymajor_name != pymajor_name_:
+                            py_deps[pymajor_name_].append(spec)
                     if legacy or legacy_Provides:
                         py_deps[legacy_name].append(spec)
         if Requires or (Recommends and dist.extras):