We report an X-ray reflectivity study on highly charged lamellar phases of the surfactant didodecyldimethylammonium halides (DDA+X- where X- = Cl- or Br-). A few thousand bilayers are aligned on a flat solid surface with a mosaicity below 0.01° and are swollen under controlled osmotic pressure (Π) from periodicities (d) of a few nanometers up to several tens of nanometers by means of direct immersion in the osmotic stressor reservoir. The high-pressure regime (small d) is obtained by water vapor of controlled relative humidity, while lower pressures (high d) are imposed by means of a novel osmotic stress technique. Accordingly, the solid supported sample is immersed in a high mass polyelectrolyte solution with the same sign and counterions than the membranes under study. Thus, water equilibrating time is reduced from weeks to minutes due to the absence of a semipermeable dialysis membrane. Measurements of the specular and nonspecular X-ray reflectivity are demonstrated to be possible through the osmotic reservoir even with a laboratory X-ray tube which greatly simplifies the establishment of the equation of state Π(d). With the same setup, bilayer undulations and compressibility fluctuations can be studied by peak line shape analysis of high-resolution synchrotron data.