A two-step enhancement method based on spectral subtraction and phase spectrum compensation is presented in this paper for noisy speeches in adverse environments involving non-stationary noise and medium to low levels of SNR. The magnitude of the noisy speech spectrum is modified in the first step of the proposed method by a spectral subtraction approach, where a new noise estimation method based on the low frequency information of the noisy speech is introduced. We argue that this method of noise estimation is capable of estimating the non-stationary noise accurately. The phase spectrum of the noisy speech is modified in the second step consisting of phase spectrum compensation, where an SNR-dependent approach is incorporated to determine the amount of compensation to be imposed on the phase spectrum. A modified complex spectrum is obtained by aggregating the magnitude from the spectral subtraction step and modified phase spectrum from the phase compensation step, which is found to be a better representation of enhanced speech spectrum. Speech files available in the NOIZEUS database are used to carry extensive simulations for evaluation of the proposed method.