The Collaborative International Dictionary of English v.0.48:

Promptly \Prompt"ly\, adv.
   In a prompt manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

promptly
    adv 1: with little or no delay; "the rescue squad arrived
           promptly"; "come here, quick!" [syn: promptly,
           quickly, quick]
    2: in a punctual manner; "he did his homework promptly" [syn:
       promptly, readily, pronto]
    3: at once (usually modifies an undesirable occurrence); "he
       promptly forgot the address" [syn: promptly, right away]

Moby Thesaurus II by Grady Ward, 1.0:

104 Moby Thesaurus words for "promptly":
   PDQ, agilely, amain, animatedly, anxiously, apace, ardently,
   at flank speed, at once, avidly, breathlessly, by forced marches,
   cursorily, de bonne volonte, decisively, directly, double-quick,
   eagerly, enthusiastically, expeditiously, fast, feverishly,
   flat-out, forthwith, furiously, hand over fist, hand over hand,
   hastily, hell for leather, hell-bent, hell-bent for election,
   helter-skelter, hotfoot, hurriedly, hurry-scurry, immediately,
   impatiently, in double time, in double-quick time, in high,
   in high gear, in no time, in passing, in seven-league boots,
   instantaneously, instanter, instantly, keenly, lickety-cut,
   lickety-split, momentarily, nimbly, on the double, on the instant,
   on the run, on the spot, pell-mell, post, posthaste,
   pretty damned quick, pronto, punctually, quick, quickly, rapidly,
   readily, right away, right off, slapdash, smartly, snappily,
   speedily, spryly, straightaway, straightway, subito, summarily,
   superficially, swiftly, trippingly, under forced draft,
   vivaciously, whip and spur, willingly, with a rush, with a will,
   with alacrity, with all haste, with all speed, with dispatch,
   with giant strides, with good will, with gusto, with haste,
   with open arms, with rapid strides, with relish, with speed,
   with zest, without delay, without further delay,
   without hesitation, zealously, zestfully