Covarying phenotypic traits can limit natural selection's ability to modify these traits. Most evolutionary stud- ies on trait covariation use the comparative method to study complex traits of multicellular organisms. Simpler traits have the advantage of being amenable to experimental evolution. Here we study such a simple molecular system, the TEM-1 beta-lactamase protein, a promiscuous enzyme that hydrolyses antibiotics, and thus confers antibiotic resistance to bacte- ria. We mutagenized large populations of TEM-1, and selected in these populations for activity on the four different anti- biotics ampicillin, carbenicillin, oxacillin, and penicillin G. While mutagenesis alone lead to highly correlated changes in enzyme activity on the four antibiotics, subsequent selection was able to modify this activity covariation substantially, and even lead to uncorrelated activities. We found that selection on one antibiotic A may be more effective in increasing activ- ity on another antibiotic B then selection on antibiotic B itself. We call this phenomenon phenotypic hitchhiking. It can be readily explained through quantitative genetic theory as a consequence of differing variances in covarying traits. It may help engineer macromolecules with desirable properties through directed evolution. Our analysis is a first step towards systematic analysis of trait covariation in experimental molecular systems. It shows that selection may readily modify the phenotypic constraints that limit its efficacy.