|Abstract:||Directionality effects in the parsing of rhythmical secondary stress are analyzed in this paper as the result of two conflicting types of constraints. A dominant alignment constraint ALLFTL, requiring feet to be aligned as much as possible to the left edge of the prosodic word, is responsible for the generation of metrical structures were feet are left-aligned. Right-alignment, on the other hand, is not the result of an alignment constraint, but the consequence of the rhythmical constraints *CLASH and *LAPSE demanding alternating rhythm. This approach to directionality makes the right typological predictions excluding from the set of possible metrical structures right-aligning iambic systems, which are not attested among the world's languages. The interaction between the constraints determining rhythmical secondary stress and the constraints determining main stress placement is discussed and it is shown how one more typological observation, the non-existence of initial dactyl systems, is predicted by the system. A detailed analysis of quantity-sensitive patterns shows that the same constraints that determine directionality in quantity-insensitive languages generate the attested patterns and fail to generated the non-attested ones also in quantity-sensitive systems. Finally, although constraints like *CLASH and *LAPSE make similar demands requiring strict alternation of rhythm, at more careful scrutiny it turns out that they cannot be unified in a general constraint demanding alternating stress.