Intense and ultrashort x-ray pulses from free-electron lasers open up the possibility for near-atomic resolution imaging without the need for crystallization. Such experiments require high photon fluences and pulses shorter than the time to destroy the sample. We describe results with a new femtosecond pump-probe diffraction technique employing coherent 0.1 keV x rays from the FLASH soft x-ray free-electron laser. We show that the lifetime of a nanostructured sample can be extended to several picoseconds by a tamper layer to dampen and quench the sample explosion, making <1 nm resolution imaging feasible.