  In a voting problem with a finite set of alternatives to choose from, we
study the manipulation of tops-only rules. Since all non-dictatorial (onto)
voting rules are manipulable when there are more than two alternatives and all
preferences are allowed, we look for rules in which manipulations are not
obvious. First, we show that a rule does not have obvious manipulations if and
only if when an agent vetoes an alternative it can do so with any preference
that does not have such alternative in the top. Second, we focus on two classes
of tops-only rules: (i) (generalized) median voter schemes, and (ii) voting by
committees. For each class, we identify which rules do not have obvious
manipulations on the universal domain of preferences.
