I tried to use timebin fits to get to the residuals.

In short, it didn't improve things.

The first issue is the stability of the fiits for low amplitudes.

To check that, I show the correlation of the amplitude with the adc sum. The expectation is a strong corellation with some excess towards higher amplitudes for cases where some of the pulse is cut off.

I distinguish for the strip with the maximum ADC and the other ones. It turns out that the side strips are more difficult to fit.

Here are the correlation with 1/\tau not fixed

Same of the side strips.

The correlation becomes much better if 1/\tau is fixed to 0.55:

Max Strips:

And for the side Strips, but still at low charges a lot of smearing

However, the residuals actually grow, roughly by a factor of 1.5.

So here is the residua plot for fixed \tau:

If I do not fix \tau it is even worse.