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In this paper, design rules for optimal silicon Raman amplifiers operating at standard telecommunications wavelengths are formulated. For given material and waveguide parameters, and a specified upper pump-power limit, explicit expressions are derived for the optimal length and maximum possible gain of single-pass-pumped amplifiers. For ring-resonator (RR) amplifiers, the optimization problem is reduced to finding a zero of a fifth-order polynomial. Due to resonant pump-power enhancement, RR amplifiers with positive gain can be realized for any pump power, however small it is. Finally, for small pump powers, the maximum possible gain is most effectively increased by reducing the linear waveguide losses as opposed to the effective area or the effective free-carrier lifetime.