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The following paper deals with the estimation of partial parameters for non stationary sinusoids. First the existing bias for the analysis of non stationary sinusoids in a standard estimator is discussed. Then a new approach to bias reduction is proposed that consists of frequency slope estimation and demodulation to reduce the bias of the standard parameter estimator. The new approach does not require the use of Gaussian analysis windows. We present an experimental evaluation that compares the new parameter estimation scheme with previously existing methods. The results demonstrate that the bias is significantly reduced to a level that is similar or lower than the bias that exists for Gaussian analysis windows. The parameter range for which significant bias reduction can be achieved is increased.