Tyre sizes and choices for Supermoto

[Glynn123]

Hi everyone, just back from a brilliant day of racing on twisties up a mountain pass, DT performed brilliantly and for the first time I could 100% tell the massive difference the USD conversion has made to the bike, no dive under braking and very planted through the corners, the little DT screaming down the pass was keeping up with a Ducati multistrada, although it was completely left on the straights haha.
Im having a problem with tyre sizes and profiles right now, currently I just threw any old tyre on the rear as I needed the bike going for summer, and havent had the money to change it yet. Currently ive got a nice Conti Attack SM 120 tyre on the front, very aggressive profile and feels brilliant in the corners, but the rear is massively letting me down. Its got a pretty much squared off Pilot Street 130 tyre, the profile is definitely too narrow for the rim and ive got pleanty space between the swingarm, it doesnt have much curvature, or atleast none compared to the front tyre, and its making the bike difficult to lean.

What tyres and sizes do people run on these things? id like to order a new Conti Attack SM 150 tyre for the rear as id say itll match the profile of the front well, but maybe this is too wide for the standard DTX/WRX 125 rims as I think the rear is 3.50?
Whats everyones opinion,
Cheers