Modern X-Ray Free-Electron Lasers (XFEL) are a key tool to enable a variety of scientific research. Those large-scale machines rely on robust and reliable deep ultraviolet (DUV) laser sources to drive electrons from their RF photocathode gun. In this paper we present a new photocathode laser prototype, which offers more flexibility in duration and shape of the 257.5 nm pulses for driving the CsTe Photocathodes of DESY’s superconducting burst-mode FELs. The laser matches the FEL pulse structure, which are 800 µs bursts at up to 4.5 MHz intraburst-rate with 10 Hz burst-repetition-rate. In a first version the system will offer variable DUV pulse durations, tunable from 1 ps to 20 ps to address different operational regimes of the XFEL. The laser system comprises a high-resolution spectral shaper with the option of generating flat-top DUV pulses for reducing electron-beam emittance at a later version. The laser is constructed in a hybrid Yb:fiber and Yb:YAG architecture. Our prototype delivers 180 uJ pulse energy at 1030 nm and 1 MHz intra-burst rate and we demonstrated conversion of 50µJ of the NIR beam to DUV, resulting 11.5µJ at 21ps (FWHM) and 6.15 µJ at 1.05 ps (FWHM) pulse duration