  We study a solar spicule observed off-limb using high-resolution imaging
spectroscopy in the Ca II 8542 \AA\ line obtained with the CRisp Imaging
SpectroPolarimeter (CRISP) on the Swedish 1-m Solar Telescope. Using a new
version of the non-LTE code NICOLE specifically developed for this problem we
invert the spicule single- and double-peak line profiles. This new version
considers off-limb geometry and computes atomic populations by solving the 1D
radiative transfer assuming a vertical stratification. The inversion proceeds
by fitting the observed spectral profiles at 14 different heights with
synthetic profiles computed in the model by solving the radiative transfer
problem along its length. Motivated by the appearance of double-peak Ca II 8542
\AA\ spicule profiles, which exhibit two distinct emission features well
separated in wavelength, we adopt a double-component scenario. We start from
the ansatz that the spicule parameters are practically constant along the
spicule axis for each component, except for a density drop. Our results support
this ansatz by attaining very good fits to the entire set of 14$\times$4
profiles (14 heights and 4 times). We show that the double-component model with
uniform temperature of 9560 K, exponential decrease of density with a height
scale of $1000-2000$ km, and the counter-oriented line-of-sight velocities of
components reproduce the double-peak line profiles at all spicule segments
well. Analyses of the numerical response function reveals the necessity of the
inversions of spectra at multiple height positions to obtain height-dependent,
degeneracy-free reliable model with a limited number of free parameters.
