The Collaborative International Dictionary of English v.0.48:

Reconstruct \Re`con*struct"\ (-str?kt"), v. t.
   To construct again; to rebuild; to remodel; to form again or
   anew.
   [1913 Webster]

         Regiments had been dissolved and reconstructed.
                                                  --Macaulay.
   [1913 Webster]

WordNet (r) 3.0 (2006):

reconstruct
    v 1: reassemble mentally; "reconstruct the events of 20 years
         ago" [syn: reconstruct, construct, retrace]
    2: build again; "The house was rebuild after it was hit by a
       bomb" [syn: rebuild, reconstruct]
    3: cause somebody to adapt or reform socially or politically
    4: return to its original or usable and functioning condition;
       "restore the forest to its original pristine condition" [syn:
       restore, reconstruct]
    5: do over, as of (part of) a house; "We are remodeling these
       rooms" [syn: remodel, reconstruct, redo]

Moby Thesaurus II by Grady Ward, 1.0:

85 Moby Thesaurus words for "reconstruct":
   accommodate, adapt, adjust, alter, ameliorate, better, break up,
   change, convert, copy, deform, denature, diversify, do over, do up,
   doctor, duplicate, fit, fix, improve, make over, meliorate,
   mitigate, modify, modulate, mutate, overhaul, overthrow, patch,
   qualify, re-create, re-form, readjust, realign, rearrange,
   reassemble, rebuild, reclaim, recondition, reconstitute, recover,
   redesign, redo, reestablish, refabricate, refashion, refit, reform,
   refound, regenerate, rehabilitate, reinstitute, reissue,
   rejuvenate, remake, remodel, renew, renovate, reorder, reorganize,
   repair, repeat, reprint, reproduce, reshape, reshuffle, restitute,
   restore, restructure, resurrect, retool, revamp, revise, revive,
   ring the changes, shift the scene, shuffle the cards, subvert,
   turn the scale, turn the tables, turn the tide, turn upside down,
   vary, work a change, worsen