We summarize the results of a 20-yr campaign to study the light curves of BK Lyn, a nova-like star strangely located below the 2 to 3 h orbital-period gap in the family of cataclysmic variables (CVs). Two apparent superhumps dominate the nightly light curves, with periods 4.6 per cent longer, and 3.0 per cent shorter, than the orbital period. The first appears to be associated with the star's brighter states (V ∼ 14), while the second appears to be present throughout and becomes very dominant in the low state (V ∼ 15.7). It is plausible that these arise, respectively, from a prograde apsidal precession and a retrograde nodal precession of the star's accretion disc. Starting in the year 2005, the star's light curve became indistinguishable from that of a dwarf nova – in particular, that of the ER UMa subclass. No such clear transition has ever been observed in a CV before. Reviewing all the star's oddities, we speculate: (a) BK Lyn is the remnant of the probable nova on 101 December 30, and (b) it has been fading ever since, but it has taken ∼2000 yr for the accretion rate to drop sufficiently to permit dwarf-nova eruptions. If such behaviour is common, it can explain other puzzles of CV evolution. One: why the ER UMa class even exists (because all members can be remnants of recent novae). Two: why ER UMa stars and short-period nova-likes are rare (because their lifetimes, which are essentially cooling times, are short). Three: why short-period novae all decline to luminosity states far above their true quiescence (because they are just getting started in their post-nova cooling). Four: why the orbital periods, accretion rates and white dwarf temperatures of short-period CVs are somewhat too large to arise purely from the effects of gravitational radiation (because the unexpectedly long interval of enhanced post-nova brightness boosts the mean mass-transfer rate). And maybe even five: why very old, post-period-bounce CVs are hard to find (because the higher mass-loss rates have ‘burned them out’). These are substantial rewards in return for one investment of hypothesis: that the second parameter in CV evolution, besides orbital period, is time since the last classical-nova eruption.