diff --git a/README.md b/README.md
index b5c8dfa0291cef1299fb41bf22d9ed0d1cca385d..60356af941d43e5f8d3649a67ff392b5771aa751 100644
--- a/README.md
+++ b/README.md
@@ -87,6 +87,7 @@ To try this out you will need: python 3, cython
     compilation for you, you can by the way see the C code generated
     in test.c, the function call starts something like:
 
+        :::C
         static double __pyx_f_4test_integrand(CYTHON_UNUSED int __pyx_v_n, double *__pyx_v_args)
 
     [`CYTHON_UNUSED` _I think_ because the argument n is not used in `integrand()`, but the standard rubric for `LowLevelCallable.from_cython()` needs it]
@@ -115,6 +116,77 @@ I didn't quite figure out how to make this work with NumPy data
 types. But maybe that doesn't matter.
 
 
+
+Update 7.4.2020: some tips on getting Cython to generate native C code
+----------------------------------------------------------------------
+
+1.  If you employ float division, use the Cython decorator
+    `@cython.cdivision(True)` before a `cdef` function:
+
+        import cython
+		
+		...
+
+        # The decorator stops division by zero checking
+        @cython.cdivision(True)
+		cdef double C1(double t, double t_cut, double t_0):
+
+            ... etc ...
+
+    to avoid Python checking for a `DivisionByZeroError`. Note that
+    you will need `import cython` to get access to this decorator.
+	
+2.  You can find [Cython version of Scipy special
+    functions](https://docs.scipy.org/doc/scipy/reference/special.cython_special.html)
+    in `scipy.special.cython_special`, for the Bessel function
+    normally given by [`scipy.special.jv`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.jv.html)
+    we needed to do:
+	
+        from scipy.special.cython_special cimport jv
+
+3.  Similarly, Cython makes available C versions of many common C
+    library functions ([read more
+    here](https://cython.readthedocs.io/en/latest/src/tutorial/external.html)):
+
+        from libc.math cimport sqrt, exp, sin, cos
+		
+4.  Note that although Cython knows about the C99 complex numbers, I
+    still haven't quite worked out how to do fast mathematics with
+    them directly (but using the real and imaginary parts separately
+    is ok).
+	
+5.  Keep checking the yellow-highlighted 'annotation' HTML file Cython
+    generates, and don't panic if something is still yellow (meaning
+    it may be calling interpreted Python still). Click the `+` to the
+    left of the line number to see what is actually happening.
+	
+	Even after doing the above things, we were using 
+	
+	    :::python
+	    return result.real
+	
+	which led to some yellow highlighting. But the underlying code
+    contained the following preprocessor stuff:
+	
+
+		#if CYTHON_CCOMPLEX
+		  #ifdef __cplusplus
+			#define __Pyx_CREAL(z) ((z).real())
+			#define __Pyx_CIMAG(z) ((z).imag())
+		  #else
+			#define __Pyx_CREAL(z) (__real__(z))
+			#define __Pyx_CIMAG(z) (__imag__(z))
+		  #endif
+		#else
+			#define __Pyx_CREAL(z) ((z).real)
+			#define __Pyx_CIMAG(z) ((z).imag)
+		#endif
+	
+	Comparing this with [the GCC
+    documentation](http://gcc.gnu.org/onlinedocs/gcc/Complex.html), it
+    seems we are generating native C code after all, but Cython can't
+    tell that.
+
 Further reading
 ---------------
 
@@ -137,3 +209,9 @@ Further reading
     Cython](https://stackoverflow.com/questions/4495420/passing-numpy-arrays-to-c-code-wrapped-with-cython)
     is a StackOverflow question of potential reference to getting
     NumPy to play along.
+
+*   [Introduction to Cython for Solving Differential
+    Equations](http://hplgit.github.io/teamods/cyode/main_cyode.html)
+    by Hans Petter Langtangen does not cover the
+    scipy.LowLevelCallable integration, but has lots of other useful
+    tidbits.