CMOS pixel sensors with a small collection electrode combine the advantages of a small sensor capacitance with the advantages of a fully monolithic design. The small sensor capacitance results in a large ratio of signal-to-noise and a low analogue power consumption, while the monolithic design reduces the material budget, cost and production effort. However, the low electric field in the pixel corners of such sensors results in an increased charge collection time, that makes a fully efficient operation after irradiation and a timing resolution in the order of nanoseconds challenging for pixel sizes larger than approximately forty micrometers. This paper presents the development of concepts of CMOS sensors with a small collection electrode to overcome these limitations, using three-dimensional Technology Computer Aided Design simulations. The studied design uses a 0.18 μm process implemented on a high-resistivity epitaxial layer.