The string effective action at tree level contains, in its bosonic sector, the Einstein-Hilbert term, the dilaton, and the axion, besides scalar and gauge fields coming from the Ramond-Ramond sector. The reduction to four dimensions brings to scene moduli fields. We generalize this effective action by introducing two arbitrary parameters, ω and m, connected with the dilaton and axion couplings. In this way, more general frameworks can be analyzed. Regular solutions with a bounce can be obtained for a range of (negative) values of the parameter ω which, however, exclude the pure string configuration (ω = −1). We study the evolution of scalar perturbations in such cosmological scenarios. The predicted primordial power spectrum decreases with the wavenumber with spectral index ns = −2, in contradiction with the results of the W M AP . Hence, all such effective string motivated cosmological bouncing models seem to be ruled out, at least at the tree level approximation.