We investigate two approaches for the spectral broadening and compression of 1-ps long pulses of a thin-disk laser amplifier running at 50 kHz repetition rate at 1030 nm wavelength. We find that with a single, 2.66-m long stretched flexible hollow fiber filled with xenon gas, Fourier transform limited output pulse duration of 66 fs can be directly reached. For larger pulse shortening, we applied a hybrid cascaded approach involving a BBO-based pre-compressor and a long hollow fiber. We could achieve 33-times temporal shortening of 1-ps pulses down to a duration of 30 fs at an overall efficiency of similar to 29% with an output power level of 3.7 W. These results demonstrate the potential of stretched flexible fibers with their free length scalability for shortening laser pulses of moderate peak power.