Fourier decomposition is a well established technique used in stellar pulsation .
However the quality of reconstructed light curves using this method is reduced when the observed data have uneven phase coverage .
We use simulated annealing techniques together with Fourier decomposition to improve the quality of the Fourier decomposition for many OGLE LMC fundamental mode Cepheids .
This method restricts the range that Fourier amplitudes can take .
The ranges are specified by well sampled Cepheids in the Galaxy and Magellanic Clouds .

We also apply this method to reconstructing Cepheid light curves observed by the HST .
These typically consist of 12 V band and 4 I band points .
We employ a direct Fourier fit to the 12 V band points using the simulated annealing method mentioned above and explicitly derive and use Fourier interrelations to reconstruct the I band light curve .
We discuss advantages and drawbacks of this method when applied to HST Cepheid data over existing template methods .
Application of this method to reconstruct the light curves of Cepheids observed in NGC 4258 shows that the derived Cepheid distance ( \mu _ { 0 } = 29.38 \pm 0.06 , random error ) is consistent with its geometrical distance ( \mu _ { 0 } = 29.28 \pm 0.09 ) derived from observations of water maser .