The Collaborative International Dictionary of English v.0.48:

Air-tight \Air"-tight`\, a.
   1. So tight as to be impermeable to air or other gases; as,
      an air-tight cylinder; -- said of containers.
      [1913 Webster]

   2. of such close construction as to have little leakage of
      air in or out; -- said of structures
      [WordNet 1.5]

   3. so thoroughly convincing as to be insusceptible to doubt;
      having no apparent counterarguments; -- of arguments or
      assertions an airtight alibi an airtight argument

   Syn: airtight, uncontradictable, undeniable.
        [PJC]

The Collaborative International Dictionary of English v.0.48:

Air-tight \Air"-tight`\, n.
   A stove the draft of which can be almost entirely shut off.
   [Colloq. U. S.]
   [1913 Webster]

WordNet (r) 3.0 (2006):

airtight
    adj 1: having no weak points; "an airtight defense"; "an
           airtight argument" [syn: airtight, air-tight]
    2: not allowing air or gas to pass in or out [syn: airtight,
       air-tight, gas-tight]

Moby Thesaurus II by Grady Ward, 1.0:

53 Moby Thesaurus words for "airtight":
   ballproof, bombproof, bulletproof, burglarproof, close, compact,
   corrosionproof, dampproof, dustproof, dusttight, fast,
   fire-resisting, fireproof, firm, flameproof, foolproof, gasproof,
   gastight, hermetic, hermetically sealed, holeproof, impervious to,
   leakproof, lightproof, lighttight, noiseproof, oilproof, oiltight,
   proof, proof against, punctureproof, rainproof, raintight,
   resistant, rustproof, sealed, shatterproof, shellproof, shut fast,
   smokeproof, smoketight, snug, soundproof, staunch, stormproof,
   stormtight, tight, water-repellant, waterproof, watertight,
   weatherproof, windproof, windtight