  The light curves from a variety of celestial objects display aperiodic
variations, often giving rise to red-noise components in their power spectra.
Searching for a narrow power spectrum peak resulting from a periodic modulation
over the frequency range in which ``coloured'' noise components are dominant
has proven a very complex task. We develop here a technique aimed at detecting
periodicities in the presence of ``coloured'' power spectrum components, while
mantaining the highest Fourier frequency resolution. First we introduce a
simple approximation to the statistical properties of the ``coloured'' power
spectra from celestial objects, based on a few examples and the theory of
linear processes. We then estimate the continuum components in the power
spectrum through an ad hoc smoothing technique. By dividing the sample spectrum
by the smoothed one, a white-noise like spectrum is obtained, the approximate
probability distribution of which is derived. A search for coherent pulsations
is then carried out by looking for peaks in the divided spectrum, the chance
probability of which is below a given detection threshold. The technique is
tested and its range of applicability determined through extensive numerical
simulations. We present also an application to the X-ray light curves of
V0332+53, a highly variable accreting X-ray pulsar, and GX13+1, a bright and
variable accreting source in the galactic bulge.
