We propose and demonstrate a new approach to implement a wavelength-tunable ultrafast fiber laser source suitable for multiphoton microscopy. We employ fiber-optic nonlinearities to broaden a narrowband optical spectrum generated by an Yb-fiber laser system and then use optical bandpass filters to select the leftmost or rightmost spectral lobes from the broadened spectrum. Detailed numerical modeling shows that self-phase modulation dominates the spectral broadening, self-steepening tends to blue shift the broadened spectrum, and stimulated Raman scattering is minimal. We also find that optical wave breaking caused by fiber dispersion slows down the shift of the leftmost/rightmost spectral lobes and therefore limits the wavelength tuning range of the filtered spectra. We show both numerically and experimentally that shortening the fiber used for spectral broadening while increasing the input pulse energy can overcome this dispersion-induced limitation; as a result, the filtered spectral lobes have higher power, constituting a powerful and practical approach for energy scaling the resulting femtosecond sources. We use two commercially available photonic crystal fibers to verify the simulation results. More specific, use of 20-mm fiber NL-1050-ZERO-2 enables us to implement an Yb-fiber laser based ultrafast source, delivering femtosecond (70-120 fs) pulses tunable from 825 nm to 1210 nm with >1 nJ pulse energy.