Ok, now I've found some examples that work from a bona fide grammar site:http://www.edufind.com/english/grammar/IF9.cfm
Unless means the same as if...not. Like if, it is followed by a present tense, a past tense or a past perfect (never by 'would'). It is used instead of if + not in conditional sentences of all types:
Type 1: (Unless + present)
a. You'll be sick unless you stop eating. (= You will be sick if you don't stop eating)
b. I won't pay unless you provide the goods immediately. (= If you don't provide them I won't pay)
c. You'll never understand English unless you study this grammar carefully. (= You'll never understand if you don't study...)
Type 2: (Unless + past)
a. Unless he was very ill, he would be at work.
b. I wouldn't eat that food unless I was really hungry.
c. She would be here by now unless she was stuck in the traffic.
Type 3: (Unless + past perfect)
a. The elephant wouldn't have seen the mouse unless she'd had perfect eyesight.
b. I wouldn't have phoned him unless you'd suggested it.
c. They would have shot her unless she'd given them the money.
(So the past perfect apparently only didn't work with my particular example - because it didn't make sense.)