Understanding and controlling the molecular organization of amphiphilic molecules at interfaces is essential for materials and biological sciences. When spread on water, the model amphiphiles constituted by C(n)F(2n+1)C(m)H(2m+1) (FnHm) diblocks spontaneously self-assemble into surface hemimicelles. Therefore, compression of monolayers of FnHm diblocks is actually a compression of nanometric objects. Langmuir films of F8H16, F8H18, F8H20, and F10H16 can actually be compressed far beyond the "collapse" of their monolayers at approximately 30 A(2). For molecular areas A between 30 and 10 A(2), a partially reversible, 2D/3D transition occurs between a monolayer of surface micelles and a multilayer that coexist on a large plateau. For A<10 A(2), surface pressure increases again, reaching up to approximately 48 mN m(-1) before the film eventually collapses. Brewster angle microscopy and AFM indicate a several-fold increase in film thickness when scanning through the 2D/3D coexistence plateau. Compression beyond the plateau leads to a further increase in film thickness and, eventually, to film disruption. Reversibility was assessed by using compression-expansion cycles. AFM of F8H20 films shows that the initial monolayer of micelles is progressively covered by one (and eventually two) bilayers, which leads to a hitherto unknown organized composite arrangement. Compression of films of the more rigid F10H16 results in crystalline-like inflorescences. For both diblocks, a hexagonal array of surface micelles is consistently seen, even when the 3D structures eventually disrupt, which means that this monolayer persists throughout the compression experiments. Two examples of pressure-driven transformations of films of self-assembled objects are thus provided. These observations further illustrate the powerful self-assembling capacity of perfluoroalkyl chains.