Apparently, I've been tying my shoes the wrong way all my life—turning them into a granny knot, which is more prone to slip. (And indeed, I had grown used to typine the loops into a double knot to prevent that.)
conuly pointed me, indirectly, to http://www.fieggen.com/shoelace/slipping.htm, which convinced me (FWIW, I fall under the "Standard Shoelace Knot, Start: Left end over Right end & through, Finish: Right loop, Left end around Front" category).
So perhaps I shall either tie my starting knot the other way around (as Ian recommends), or learn a completely different knot, such as the "Ian Knot".
Geek heaven, especially in the "deep interest in a narrow field of endeavour" sense of the word "geek".