diff --git a/libsemanage/src/Makefile b/libsemanage/src/Makefile
index 7acf63d..cdd8388 100644
--- a/libsemanage/src/Makefile
+++ b/libsemanage/src/Makefile
@@ -1,9 +1,15 @@
+# Support building the Python bindings multiple times, against various Python
+# runtimes (e.g. Python 2 vs Python 3) by optionally prefixing the build
+# targets with "PYPREFIX":
+PYTHON ?= python
+PYPREFIX ?= 
+
 # Installation directories.
 PREFIX ?= $(DESTDIR)/usr
 LIBDIR ?= $(PREFIX)/lib
 SHLIBDIR ?= $(PREFIX)/lib
 INCLUDEDIR ?= $(PREFIX)/include
-PYLIBVER ?= $(shell python -c 'import sys;print "python%d.%d" % sys.version_info[0:2]')
+PYLIBVER ?= $(shell $(PYTHON) -c 'import sys;print("python%d.%d" % sys.version_info[0:2])')
 PYINC ?= /usr/include/${PYLIBVER}
 PYLIBDIR ?= $(LIBDIR)/${PYLIBVER}
 RUBYLIBVER ?= $(shell ruby -e 'print RUBY_VERSION.split(".")[0..1].join(".")')
@@ -34,9 +40,9 @@ SWIGIF= semanageswig_python.i
 SWIGRUBYIF= semanageswig_ruby.i
 SWIGCOUT= semanageswig_wrap.c
 SWIGRUBYCOUT= semanageswig_ruby_wrap.c
-SWIGLOBJ:= $(patsubst %.c,%.lo,$(SWIGCOUT)) 
+SWIGLOBJ:= $(patsubst %.c,$(PYPREFIX)%.lo,$(SWIGCOUT)) 
 SWIGRUBYLOBJ:= $(patsubst %.c,%.lo,$(SWIGRUBYCOUT)) 
-SWIGSO=_semanage.so
+SWIGSO=$(PYPREFIX)_semanage.so
 SWIGFILES=$(SWIGSO) semanage.py 
 SWIGRUBYSO=_rubysemanage.so
 LIBSO=$(TARGET).$(LIBVERSION)
@@ -132,7 +138,9 @@ install: all
 
 install-pywrap: pywrap 
 	test -d $(PYLIBDIR)/site-packages || install -m 755 -d $(PYLIBDIR)/site-packages
-	install -m 755 $(SWIGFILES) $(PYLIBDIR)/site-packages
+	install -m 755 $(SWIGSO) $(PYLIBDIR)/site-packages/_semanage.so
+	install -m 755 semanage.py $(PYLIBDIR)/site-packages
+
 
 install-rubywrap: rubywrap
 	test -d $(RUBYINSTALL) || install -m 755 -d $(RUBYINSTALL)