ABSTRACT CHEOPS (CHaracterising ExOPlanet Satellite) is an ESA S-class mission that observes bright stars at high cadence from low-Earth orbit. The main aim of the mission is to characterize exoplanets that transit nearby stars using ultrahigh precision photometry. Here, we report the analysis of transits observed by CHEOPS during its Early Science observing programme for four well-known exoplanets: GJ 436 b, HD 106315 b, HD 97658 b, and GJ 1132 b. The analysis is done using pycheops, an open-source software package we have developed to easily and efficiently analyse CHEOPS light-curve data using state-of-the-art techniques that are fully described herein. We show that the precision of the transit parameters measured using CHEOPS is comparable to that from larger space telescopes such as Spitzer Space Telescope and Kepler. We use the updated planet parameters from our analysis to derive new constraints on the internal structure of these four exoplanets.