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 ]

n. A stove the draft of which can be almost entirely shut off. [ Colloq. U. S. ] [ 1913 Webster ]