diff --git a/python-productmd.spec b/python-productmd.spec
index 41ee5b6..55fddb2 100644
--- a/python-productmd.spec
+++ b/python-productmd.spec
@@ -1,13 +1,10 @@
-%global with_python3 1
-
-%if 0%{?fedora} && 0%{?fedora} <= 12
-%global with_python3 0
-%endif
-
-%if 0%{?rhel} && 0%{?rhel} <= 7
-%{!?__python2: %global __python2 /usr/bin/python2}
-%{!?python2_sitelib: %global python2_sitelib %(%{__python2} -c "from distutils.sysconfig import get_python_lib; print(get_python_lib())")}
-%global with_python3 0
+# Enable Python 3 builds for Fedora + EPEL >5
+%if 0%{?fedora} || 0%{?rhel} > 5
+# If the definition isn't available for python3_pkgversion, define it
+%{?!python3_pkgversion:%global python3_pkgversion 3}
+%bcond_without  python3
+%else
+%bcond_with     python3
 %endif
 
 # compatibility with older releases
@@ -19,7 +16,7 @@
 
 Name:           python-productmd
 Version:        1.4
-Release:        1%{?dist}
+Release:        2%{?dist}
 Summary:        Library providing parsers for metadata related to OS installation
 
 Group:          Development/Tools
@@ -38,9 +35,9 @@ BuildRequires:  python-setuptools
 BuildRequires:  python-six
 
 %if  0%{?with_python3}
-BuildRequires:  python3-devel
-BuildRequires:  python3-setuptools
-BuildRequires:  python3-six
+BuildRequires:  python%{python3_pkgversion}-devel
+BuildRequires:  python%{python3_pkgversion}-setuptools
+BuildRequires:  python%{python3_pkgversion}-six
 %endif
 
 BuildArch:      noarch
@@ -50,12 +47,12 @@ Python library providing parsers for metadata related to composes
 and installation media.
 
 %if 0%{?with_python3}
-%package -n python3-productmd
+%package -n python%{python3_pkgversion}-productmd
 Summary:       Library providing parsers for metadata related to OS installation
 Group:         Development/Tools
-Requires:      python3-six
+Requires:      python%{python3_pkgversion}-six
 
-%description -n python3-productmd
+%description -n python%{python3_pkgversion}-productmd
 Python library providing parsers for metadata related to composes
 and installation media.
 %endif
@@ -95,7 +92,7 @@ and installation media.
 
 
 %if 0%{?with_python3}
-%files -n python3-productmd
+%files -n python%{python3_pkgversion}-productmd
 %license LICENSE
 %doc AUTHORS
 %{python3_sitelib}/productmd/
@@ -103,6 +100,9 @@ and installation media.
 %endif
 
 %changelog
+* Fri Feb 10 2017 Adam Williamson <awilliam@redhat.com> - 1.4-2
+- Enable Python 3 build for EL 6+
+
 * Tue Jan 10 2017 Lubomír Sedlář <lsedlar@redhat.com> 1.4-1
 - Fix loading variants from legacy composeinfo. (dmach@redhat.com)
 - Fix sorting composes (lsedlar@redhat.com)