Resonance cancellation--use tfestimate or yulewalk?

I have some data from two generations of an ultrasound transducer. The first generation was relatively flat in frequency response, and output sharp pulses with a couple of cycles of ringing. The new ones have a peaked response with ~20 cycles of ringing, using the same input. I'm trying to design a filter that will 'correct' for this ringing, with little success so far. One approach I tried was to use tfestimate taking the old transducer signal as an input and the new one as an output, then converting that frequency response into an all-zero filter, then inverting that to an all-pole filter and applying that to the new transducer output. The results so far have not been promising with the choice of window and fft length/overlap that puts about 7 windows in my signal. Alternatively, I could model the new transducer output as an all-pole AR(n) process, and try to invert that. Problem is, the stimulus for the signal output I have is not a single impulse, but a series of reflected impulses. I think this will have undesirable effects in yulewalk.

Anyone care to suggest a better approach, perhaps involving windowing data or something similar?

Thanks