I feel MOST STRONGLY the O.G. "Pitbull" std/med (internal Clearance approx. 4.5 inch by just over 9 inches) would be best used IN PLACE of your "Series 2" (ie: As PRIMARY ANCHORING LOCK, Securing FRAME AND REAR WHEEL to a SOLID Anchoring Object) both for it's large internal clearances (vulnerable to mini hydraulic jack, unless void is filled with Expensive and Fragile bike parts) and also Being the STRONGER Lock (14 mm dual locking u shackle, O.G. X4P locking system, same tech used by O.G. "Brute") vs Big 'K's "Series 2" (weaker 13 mm single side locking u shackle, Big 'K's older less secure 'bent foot' system, same tech used by Big "K"s "Keeper").
Move the "Series 2" to Front Wheel security duty, as well as Secondary Anchoring Lock (when your "Spidey Sense"/paranoia starts tingling)
O.P., My apologies for not being able to give a better answer to your question. As you didn't give any specifics for the lock you are now using (is it a "Series 2" mini 5, mini 7, mini Long Shackle (mini LS), or "Series 2" Standard (internal clearance approx. 4 inches by 9 inches), Std. Long Shackle, Series 2 ATB?
I am also hobbled by not having a clue as to your bike (type, new/old, tire size, minimal/non aero frame/rims vs deep aero/Time Trial frame/wheels, fenders, Make, Model, year, picture would REALLY Help).

Oh, just to be clear, if the measurements are the same then they should be the same lock. Standard or Medium (terms are interchangeable, decided by the seller) U-locks have INSIDE SHACKLE measurements of approx. 4 to 4.5 inches wide by 8 to 9 inches tall.