Two slightly shifted gratings are inscribed, one over the other, while exploiting fiber strain in a single-mode fiber. The inscription is done with a near-infrared femtosecond laser, a phase mask, and a cylindrical focusing lens. The first fiber Bragg grating (FBG) is inscribed under normal fiber tension, while the second overlapping FBG is inscribed under higher fiber tension. The transmission spectrum of the complex structure is similar to that of a phase-shifted grating, yet the fabrication process is much faster and simpler compared to other standard methods. A high-quality phase-shifted grating with two -30 dB transmission dips, a 25 dB transmission peak, and <50 pm transmission bandwidth is achieved. We observe polarization-dependent transmission in the phase-shifted gratings.