i have run my at853a's with the 8531 batterybox/p48 adapter as well as my current 8533 p48 adapters.
the 8531 were pretty much useless for anything i needed them to do. only providing 1.5v of power to mic is IMO not really powering these mics. as a p48 adapter they are (as previously mentioned) the size of a pack of cigs and need a XLR break out cable if you are going to run into a pre. in sum, they underpowered the mics and were too bulky.
on the advice of a member here (i think marc kim) i sent my 8531 boxes to AT and had them send me 8533's instead. Since the 8531's were practically new, it was free of charge (other than the cost to ship to AT). These are the p48 barrels that everyone in familar with. i use these for p48 applications and had a battery box for smaller discrete needs. these days, i havent really powered the at853a's with anything other than the SD MP-2.