After contact with water, surfactant lamellar phases (LR) can show spectacular interface instabilities: multibilayer tubules, so-called myelins, grow from the LR/water interface into the water. We have studied the shape, size, and growth of myelins in aqueous solutions of the nonionic surfactant C12E3 (triethylene glycol monododecyl ether) during dissolution. We used a combination of different imaging techniques: optical microscopy providing 2-D projections of the sample and confocal microscopy offering a complete 3-D reconstruction. These techniques provide quantitative information on the shape and growth of myelins, such as their width, length, and depth profile as a function of time. The growth rate of myelins, characterized by a swelling or diffusion coefficient, was found to increase with surfactant mass fraction and, seemingly, with sample thickness. We demonstrate that myelin creaming due to buoyancy can explain the apparent dependence on sample thickness. Our experiments furthermore suggest that myelin growth is controlled by an interplay between the water mobility in the lamellar phase and the osmotic pressure difference between the lamellar phase and the contacting water.