Data words are an extension of traditional strings that have at each position, besides a symbol from some finite alphabet, a data value from some infinite domain. Class-memory automata constitute an automata model for data words with a decidable emptiness problem. The paper improves the previous result that class-memory automata are strictly more expressive than register automata, another automata model for data words. More specifically, it shows that weak class-memory automata, a restriction of class-memory automata introduced by Cotton-Barratt, Murawski, and Ong are strictly more powerful than the extension of register automata by a data-guessing facility. While weak deterministic class-memory automata yield a restriction of class-memory automata which is closed under Boolean operations, the paper also proposes an extension of deterministic class-memory automata with this property.