Disclosed are illumination systems especially suitable for very small data projectors, called pico projectors. The disclosed illumination systems provide high optical efficiency for projectors that need polarized light but utilize unpolarized light sources such as light-emitting diodes. Some of the disclosed illumination systems make use of light sources of different colors, and provide polarization conversion in ways based on color-selective elements of a variety of different types to convert substantially all the light emitted by the light sources to a single polarization, without increasing the effective optical extent of the source. Other disclosed illumination system provide compact ways to combine light from differently colored light sources without the use of bulky x-cube or angled dichroic elements.