The short-term evolvability of a character is closely related to its level of additive genetic variation. However, a large component of the variation in any one character may be pleiotropically linked to other characters under the influence of different selective factors. Therefore, the organization of the organism into quasi-independent modules may be an important prerequisite for evolvability. In this paper we propose to study character evolvability in terms of conditional genetic variation. By estimating the amount of genetic variation in a character, y, that is independent of other characters, x, we can assess the evolvability of y when there is stabilizing selection on x. We suggest that systematic use of conditioning may help build a picture of modular organization and quasi-independent evolvability. As an illustration, we use this approach to assess the evolvability of floral characters in Dalechampia scandens (Euphorbiaceae). Although our study population had relatively low levels of genetic variation at the outset, we find evidence that conditioning may lead to substantial further reduction in the genetic variation available for independent adaptation. This provides additional evidence that the D. scandens blossom is constrained in its short-term evolvability.