  We construct efficient banks of templates suitable for directed searches of
almost monochromatic gravitational waves originating from spinning nuetron
stars in our Galaxy in data being collected by currently operating
interferometric detectors. We thus assume that the position of the
gravitational-wave source in the sky is known, but we do not assume that the
wave's frequency and its derivatives are a priori known. In the construction we
employ simplified model of the signal with constant amplitude and phase which
is a polynomial function of time. All our template banks enable usage of the
fast Fourier transform algorithm in the computation of the maximum-likelihood
F-statistic for nodes of the grids defining the bank. We study and employ the
dependence of the grid's construction on the choice of the position of the
observational interval with respect to the origin of time axis. We also study
the usage of the fast Fourier transform algorithms with non-standard frequency
resolutions achieved by zero padding or folding the data. In the case of the
gravitational-wave signal with one spindown parameter included we have found
grids with covering thicknesses which are only 0.1%--16% larger than the
thickness of the optimal two-dimensional hexagonal covering.
