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We present a detailed experimental as well as theoretical study of vertical-cavity surface-emitting lasers (VCSELs) with and without etched surface modifications. The so-called inverted surface relief leads to a suppression of higher-order transverse modes, where measurements of output power and optical spectra show a maximum single-mode output power of 6.1 mW. For simulations, a hot-cavity model is applied, which can handle the complex electrical, thermal, and electromagnetic problems in a VCSEL structure in a fully 3-D manner. The optical characteristics of both structures, including current-dependent output power and spectral properties up to thermal rollover, are very well reproduced by the simulations. Furthermore, the evolution of the beam profile is investigated by simulations as well as spectrally resolved near-field measurements at various distances to the laser surface. Here, the simulations confirm the significantly stronger thermal guiding in the relief device indicated in the measurements.