Fitting RooDataHist with negative bins in tails

Dear RooFit experts,

I have a RooDataHist (attached to this post) describing a resonant signal. My goal is to fit it with a Double-Sided Crystal Ball to obtain the signal shape, which I plan to use in other fits later. The issue is that my signal sample accounts for some interference effects, which make a few bins in the right-side tail negative. This is cleary not good, and the fit fails, as there’s nothing like a negative PDF.
Are there any workarounds to this?

Thanks a lot and all the best,
Fabio.
rootForum

May be @jonas can help.