The quality and quantity of sleep is to a large extent determined by whether the sleep period is in alignment with the most favorable circadian time window for sleep. Misalignment results in compromised sleep. In order to determine this circadian time window, the 24-h profile of melatonin secretion is generally considered to provide the most optimal estimate. Melatonin secretion occurs only during the night, and several methods to determine its onset and offset markers have been proposed. In spite of the usefulness of determining circadian phase estimates from melatonin, its feasibility is somewhat restricted because the required number of repeated measurements comes at a high cost for compliance and laboratory assays. In addition, the complexity of some of the previously proposed methods to analyze data and obtain phase estimates may require a statistician. We here propose a set of novel functions to better describe the typical melatonin profile, which usually has a rather fixed baseline level during the day, has differences in the steepness of its rising and falling limbs, and may have a nocturnal plateau or even two peaks instead of one during the night. The functions can easily be fitted, even to incomplete or noisy melatonin data, with the most common statistical software packages, and the resulting parameters give direct information on the mentioned characteristics, which provide important additions to complete the usual restricted information on phase and amplitude. We show that the proposed curves fit better than single- to three-harmonic cosine curves to the typical melatonin profiles of both healthy subjects (n=13) and subjects diagnosed with Delayed Sleep Phase Syndrome (DSPS, n=27), Disorders of Initiating and Maintaining Sleep (DIMS, n=9), or sleep complaints not otherwise specified (n=7). Of note, because the functions provide a parsimonious description of the melatonin profile, phase estimates derived from them are more reliable (i.e., robust for noise and data loss). We illustrate that phase estimates deviate on average only by about 10 min in case of the loss of some of the data points and in case of the addition of noise. Finally, we introduce a sparse-sampling schedule tailored to capture the most important aspects of the melatonin curve. It is shown that such schedule - reducing the number of samples by more than 50% - in combination with the proposed functions results in reliable melatonin onset phase estimates, deviating only about 10 min from estimates based on 24 samples. The proposed methods strongly contribute to the feasibility, in terms of both cost and analysis availability, for researchers and clinicians to include the most reliable marker of the circadian timing system in their diagnosis and treatment evaluations.