We present a microscopic description for the response of crystalline Si nanospheres up to 10 nm in radius for various uniaxial compression levels. The behavior at low compressions closely resembles the Hertzian predictions. At higher compressions the creation of a new β-tin phase in the particle core leads to (i) volumetric changes (ii) an increase in elastic moduli, and (iii) significant hardening. Further, (iv) a reversible character of the transformation is obtained with molecular dynamics simulations. The agreement of (i)-(iv) with recent experimental findings challenges the current exclusive view of a dislocation plasticity response in somewhat larger nanoparticles. The phase-transition path should dominate in ultrasmall structures, where dislocation activity is prohibited.