We present more results of our long-term observational project to analyze the variations of the orbital period for early-type eccentric eclipsing binaries. About sixty new precise mid-eclipse times were measured or derived for three eclipsing binaries, namely V0345 Lac, YY Sgr, and DR Vul. Based on current O-C diagrams, we found in all cases that beside the typical apsidal motion the times of minima show additional cyclical changes likely caused by a third body orbiting the eclipsing pair. The new light curve solution of V0345 Lac results in a moderate orbital eccentricity (e=0.26) of this binary. The periods of apsidal motion are 1580 yr, 295 yr, and 36 yr, respectively. The relativistic contributions to the total apsidal-motion rate are small for all three eccentric binaries - about 5-14%. The third-body orbital periods are relatively short: 24 yr, 19 yr and 66 yr, and the minimal masses of third bodies are: 2.0 M☉, 0.8 M☉, and 7.2 M☉, respectively.