To this day, improvisation and variation represent two of the basic principles in the interpretation of traditional instrumental music in Slovakia. As part of the research in playing styles in traditional string and cimbal bands, the study of this phenomenon has been systematically approached mostly in relation to violinists, especially lead violin players. The study presents the results of research focused on the players of the accompanying function, in particular on the rhythmic structure of their musical performance. The basis of the rhythmic accompaniment in this type of ensemble is the repetition of a particular rhythmic motif with a relatively stable timing and dynamic structure. In many localities in Slovakia, kontra-players (accompanying violin or viola players) use to creatively complement or disrupt this continuous rhythmical framework with various rhythmic variations. I call them secondary rhythmic structures. Based on the analysis of four viola kontra-players recorded in the 1960s and in 2006 in the villages of Telgárt and Šumiac, we identify a relatively large number of particular secondary rhythmic structures. As it is shown, they are not only a means for rhythmic ornamentation or the expression of the players’ musical artistic creativity, but they also fulfill specific functions in the musical accompaniment. Moreover, the secondary rhythmic structures represent an important element of the individual playing styles in musical accompaniment and in some local musical traditions they can be considered another significant stylistic element of traditional dance music.