We present six new time-delay measurements obtained from R_c-band monitoring data acquired at the Max Planck Institute for Astrophysics (MPIA) 2.2 m telescope at La Silla observatory between October 2016 and February 2020. The lensed quasars HE 0047−1756, WG 0214−2105, DES 0407−5006, 2M 1134−2103, PSJ 1606−2333, and DES 2325−5229 were observed almost daily at high signal-to-noise ratio to obtain high-quality light curves where we can record fast and small-amplitude variations of the quasars. We measured time delays between all pairs of multiple images with only one or two seasons of monitoring with the exception of the time delays relative to image D of PSJ 1606−2333. The most precise estimate was obtained for the delay between image A and image B of DES 0407−5006, where τ_AB = −128.4_−3.8^+3.5 d (2.8% precision) including systematics due to extrinsic variability in the light curves. For HE 0047−1756, we combined our high-cadence data with measurements from decade-long light curves from previous COSMOGRAIL campaigns, and reach a precision of 0.9 d on the final measurement. The present work demonstrates the feasibility of measuring time delays in lensed quasars in only one or two seasons, provided high signal-to-noise ratio data are obtained at a cadence close to daily.