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Raman spectroscopy has become a powerful tool for microscopic analysis of organic and biological materials. When combined with optical tweezers (Raman tweezers), it allows investigating single, selected micrometric particles in their natural environment, therefore, reducing unwanted interferences from the cover plate. A general problem affecting both Raman spectrometers and Raman tweezers systems is the background caused by the environment surrounding the sample under investigation. In this paper, we report on a novel method that allows acquiring Raman spectra of a single trapped particle (polystyrene microspheres) free from any background contribution. The method is based on the use of two collinear and copropagating laser beams: the first is devoted to trapping (trap laser), while the second one is used to excite the Raman transitions (pump laser). The trap laser moves the trapped particle periodically, by means of a galvomirror, back and forth across the pump laser. The back-scattered photons are analyzed by a spectrometer and detected by a photomultiplier; finally, the resulting signal is sent to a lock-in amplifier for phase-sensitive detection. The purpose of the present work is to give a detailed description of our method and to supply a systematic study concerning the formation of the Raman signal. We trap polystyrene beads and study the dependence of the Raman signal on several parameters, such as height from the coverslip surface, the bead size, the modulation amplitude, and the pump laser intensity. Our results establish a direct and practical approach for background suppression in the spectroscopic analysis of optical trapped microsized samples.