In the case of the disc D-2, the annulus A = S-1 x {[}0, 1] and the torus T-2 we will show that if a sequence of natural numbers satisfies a certain growth rate, then there is a weak mixing diffeomorphism that is uniformly rigid with respect to that sequence. The proof is based on a quantitative version of the Anosov-Katok-method with explicitly defined conjugation maps and the constructions are done in the C-infinity-topology. Beyond that we can deduce a similar result in the real-analytic topology in the case of T-2. (C) 2015 Elsevier Inc. All rights reserved.