Adams and Dziobiak proved that any finite-to-finite universal quasivariety must be
Q-universal, and then asked whether a somewhat weaker hypothesis could lead to the same conclusion. We show that their original hypothesis cannot be weakened to its naturally extreme form.
Keywords distributive double p-algebra - variety - quasivariety -
Q-universality - relative universality - endomorphism monoid
To Professor Ale
Pultr on his 65th birthday The authors gratefully acknowledge the support of the NSERC of Canada, of the project LN00A056 of the Czech Ministry of Education, and also of the Grant Agency of Czech Republic under the grant 201/02/0148.
Special issue of Studia Logica: 
Algebraic Theory of Quasivarieties
Presented by
M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko