I have a few of what I would consider "Short" scopes.
March F 3-24×52
Premier Heritage Light Tactical 3-15×50
S&B PMII 3-20×50US
S&B PMII 5-20×50US
Tangent Theta TT315M 3-15×50
ZCO 4-20×50
Depending on use, weight, and features, they all have their pros and cons, and proper places.
If you want lightweight and high magnification, nothing compares to the March. But the glass is not in the same league as the rest of that list.
If you want lightweight, and good price, the Premier is your best bet, but most do not carry a warranty any longer. Alpha glass, awesome turrets, but "only" 12 MIL of elevation adjustment (dual turn 6 MIL turret). Hard to find nowadays too.
If you don't mind the price tag, the Tangent Theta TT315M is the new Premier. Glass is amazing, still under 29 oz., turrets are the same 12 MIL (DT 6 MIL) elevation and amazing, my mag ring is a little stiff, but a throw lever makes it fine. Not so short as to hinder mounting options either. 1st or 2nd best glass in the bunch.
S&B PMII 3-20×50 is a great choice. Big mag range, alpha glass, great turrets, low pro turrets, locking elevation w. capped windage, great function. But still fairly heavy @ 32 oz I think.
S&B PMII 5-20×50 is similar to the 3-20×50, but even shorter and lighter. All the features above. But, the mounting solutions are very limited, and I think putting one on a LA would be difficult unless you put high rings on it. Eye relief is a bit shorter too.
ZCO 4-20×50 I just mounted up last night. Heading to the range in 30 minutes, but first impression is outstanding. Heaviest of the bunch, a bit longer than the S&Bs, but glass appears amazing, Tangent Theta level, reticle (MPCT1) is the best I have seen, good mounting lengths, perfect seeming tension on mag ring, awesome tactile turrets, and best markings on the turrets I have.
