Two possible planetary nebulae have been found during a search around
hot H-rich white dwarfs. These are located close to Ton 320 and RE 173
8 + 665. Both are extremely faint, but are rather brighter in [N II] t
han Halpha. This would bring the total number of nebulae found around
independently identified hot DA white dwarfs to four, with one other a
round a PG 1159 star. In addition, we failed to detect any around six
PG 1159 stars. We suggest that this lack is very difficult to explain
if all white dwarfs undergo essentially the same evolution, each passi
ng through a PG 1159 stage. Furthermore, the most widely quoted altern
ative, in which approximately 25% undergo a late He-shell flash causin
g a brief return to the AGB, can successfully explain this only if it
produces a substantially greater delay than is currently assumed.