We study the quantum fluctuations of an optical nonlinear Schrödinger soliton after spectral filtering. The photon-number-bandwidth correlation of the emerging soliton produces squeezing in the photon number of the filtered soliton. Bandwidth oscillations caused by the interference of the soliton with the quantum-noise continuum, however, give oscillations of the photon-number squeezing and, in addition, prevent achievement of arbitrarily high values of squeezing through spectral filtering.