We show that there is a transcendental meromorphic function with an invariant Baker domain $U$ such every singular value of $f$ super-attracting periodic point. This answers question Bergweiler from 1993. also can be chosen to contain arbitrarily large round annuli, centred at zero, definite modulus. Mihaljevi\'c and the author 2013, complements recent work Bara\'nski et al concerning this ques...