Like the positive and negative poles of magnets, the prefix non- and its root words want to be attached firmly and directly.

Webster’s New World College Dictionary lists an impressive array of non- words written without benefit of hyphen: nonaligned, noncombatant, nonconformist, nondairy, noninvasive, nonjudgmental, nonpartisan, nonperson, nonproductive, nonprofit, nonrestrictive, nonstarter, nonsupport, nonverbal, nonviolence and dozens more. The exceptions come when the prefix is attached to a proper noun: non-Anglican, non-Latin, non-Muslim, non-Shakespearean, etc.

The Associated Press Stylebook used to have an extensive entry on which non- compounds should be hyphenated and which should be not, but in recent years it has largely abandoned that distinction. This reflects a tendency in English for many, but not all, hyphenated compounds to lose the hyphen. To-day and to-morrow switched over long ago. Today to baby-sit seems well on the way to becoming to babysit.

Non- is such a friendly, not so say promiscuous, prefix, that it will willingly attach itself to just about anything, noun, adjective, even another hyphenated compound. That is why AP warns against omitting the hyphen in “awkward combinations,” giving nonnuclear as an example. It’s an especially good example, because if the word fell at the end of a line, it would be hyphenated thus:

nonnu-

clear

The issue came to mind one evening last week when an article came under my hands bearing the word nonlife-threatening. I paused for a moment to consider what would threaten nonlife before inserting a hyphen: non-life-threatening.

In the main, you can safely omit the hyphen after non-, but the AP is right to warn against jarring consequences. Insert when needed.