Compensating for the phase shift introduced in a one-stage amplifier?

[Andrew]

I am operating a transimpedance amplifier for a photodiode
deliberately well past the cutoff frequency of about 40 Hz because I
want to keep the thermal noise down. A generic picture of the
frequency response is given on Figure 2b on page 2 in:
http://www.ece.utexas.edu/~slyan/archive/ee382m_spring04/notes/lecture16.pdf

I use a second stage of amplification (essentially a differentiator)
to compensate for the gain roll-off and the circuit does quite a good
job of flattening the gain curve up to about 200 kHz. It also does a
somwhat decent job of compensating for the 90° phase shift introduced in the
first stage, but not out to nearly as high a frequency. I calibrate
the circuits as carefully as I can to measure and digitally subtract
the actual phase shift because it turns out that any uncalibrated
phase shift is quite detrimental. I would like to design a smaller
total phase shift directly into the analog circuit.

I know how to design a circuit to compensate for the gain roll off --
matching the break points etc., but I'm not familiar with designing an analog
circuit for optimizing the nulling of the phase shift. I've read a couple of
papers on phase compensation, such as found in:
http://amsc.tamu.edu/SIS/Publications/pub/jounal/2003_6.pdf
but I don't think that's what I'm looking for. Can you provide a
tutorial for useful methods for optimizing the compensation for the
phase shift, even at the expense of an optimal compensation for the
gain rolloff?