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We present new measurements of the time delays of WFI2033−4723. The data sets used in this work include 14 years of data taken at the 1.2 m Leonhard Euler Swiss telescope, 13 years of data from the SMARTS 1.3 m telescope at Las Campanas Observatory and a single year of high-cadence and high-precision monitoring at the MPIA 2.2 m telescope. The time delays measured from these different data sets, all taken in the R -band, are in good agreement with each other and with previous measurements from the literature. Combining all the time-delay estimates from our data sets results in Δ t AB = 36.2 +0.7 −0.8 days (2.1% precision), Δ t AC = −23.3 +1.2 −1.4 days (5.6%) and Δ t BC = −59.4 +1.3 −1.3 days (2.2%). In addition, the close image pair A1-A2 of the lensed quasars can be resolved in the MPIA 2.2 m data. We measure a time delay consistent with zero in this pair of images. We also explore the prior distributions of microlensing time-delay potentially affecting the cosmological time-delay measurements of WFI2033−4723. Our time-delay measurements are not precise enough to conclude that microlensing time delay is present or absent from the data. This work is part of a H0LiCOW series focusing on measuring the Hubble constant from WFI2033−4723.