diff --git a/python/README b/python/README
index 3c7480b94b..9cca886b86 100644
--- a/python/README
+++ b/python/README
@@ -1,6 +1,6 @@
 This directory contains Python code which wraps LAMMPS as a library
 and allows the LAMMPS library interface to be invoked from Python,
-either from a script or interactively.
+either from a Python script or using Python interactively.
 
 Details on the Python interface to LAMMPS and how to build LAMMPS as a
 shared library, for use with Python, are given in
@@ -16,16 +16,22 @@ variables in your shell script.  Or you can run the python/install.py
 script directly to give you more control over where the two relevant
 files are installed.  See doc/Section_python.html for details.
 
-You can then launch Python and instantiate an instance of LAMMPS:
+You should then be able to launch Python and instantiate an instance
+of LAMMPS:
 
 % python
 >>> from lammps import lammps
 >>> lmp = lammps()
 
 If that gives no errors, you have succesfully wrapped LAMMPS with
-Python.  See doc/Section_python.html#py_5 for tests you can then use
+Python.  See doc/Section_python.html#py_7 for tests you can then use
 to run LAMMPS both in serial or parallel thru Python.
 
+Note that you can also invoke Python code from within a LAMMPS input
+script, using the "python" command.  See the doc/python.html doc page
+for details.  The Python code you invoke can also call back to LAMMPS
+using the same interface described here for wrapping LAMMPS.
+
 -------------------------------------------------------------------
 
 Once you have successfully wrapped LAMMPS, you can run the Python