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Single particle momentum spectra are calculated within three microcanonical statistical ensembles, namely, with conserved system energy, system momentum, as well as system energy and momentum. Deviations from the exponential spectrum of the grand canonical ensemble are quantified and discussed. For mean particle multiplicity and temperature, typical for p + p interactions at the LHC energies, the effect of the conservation laws extends to transverse momenta as low as about 3GeV/c. The presented results should be considered as the next step in development of statistical models for particle production in high energy collisions. They can be useful to interpret spectra measured in nuclear collisions at high energies, in particular, their system size dependence. [ABSTRACT FROM AUTHOR]