Oxide-confined vertical cavity surface emitting lasers (VCSEL) are inherently leaky structures, despite the fact that the oxidized periphery region surrounding the all-semiconductor core has a lower refractive index. The reason is that the VCSEL modes in the non-oxidized core region can be coupled to tilted modes in the selectively oxidized periphery as the orthogonality between the core mode and the modes at the periphery is broken by the oxidation-induced optical field redistribution. Engineered VCSEL designs show that the overlap between the VCSEL mode of the core and the tilted mode in the periphery can reach >30% resulting in significant leakage. Three-dimensional modeling confirms that the leakage losses are much stronger for high order transverse modes which have a higher field intensity close to the oxidized region. Single mode lasing in the fundamental mode can thus proceed up to large aperture diameters. A 850-nm GaAlAs leaky VCSEL based on this concept is designed, modeled and fabricated, showing single-mode lasing with aperture diameters up to 5 μm. Side mode suppression ratio >20dB is realized at the current density of 10kA/cm2 in devices with the series resistance of 90 Ω.