The basic building block of solar filaments/prominences is thin threads of cool plasma. We have studied the spectral properties of velocity threads, clusters of thinner density threads moving together, by analyzing a sequence of $H{alpha}$ images of a quiescent filament. The images were taken at Big Bear Solar Observatory with the Lyot filter being successively tuned to wavelengths of -0.6, -0.3, 0.0, +0.3, and +0.6 ${AA}$ from the centerline. The spectra of contrast constructed from the image data at each spatial point were analyzed using cloud models with a single velocity component, or three velocity components. As a result, we have identified a couple of velocity threads that are characterized by a narrow Doppler width($Deltalambda_D=0.27{AA}$), a moderate value of optical thickness at the $H{alpha}$ absorption peak($ au_0=0.3$), and a spatial width(FWHM) of about 1". It has also been inferred that there exist 4-6 velocity threads along the line of sight at each spatial resolution element inside the filament. In about half of the threads, matter moves fast with a line-of-sight speed of $15{pm}3km;s^{-1}$, but in the other half it is either at rest or slowly moving with a line-of-sight velocity of $0{pm}3km;s^{-1}$. It is found that a statistical balance approximately holds between the numbers of blue-shifted threads and red-shifted threads, and any imbalance between the two numbers is responsible for the non-zero line-of-sight velocity determined using a single-component model fit. Our results support the existence not only of high speed counter-streaming flows, but also of a significant amount of cool matter either being at rest or moving slowly inside the filament.