The primary purpose of the investigation was to study hypersonic, laminar, axisymmetric compression-separation with significant transverse curvature on an isothermal, but slightly cooled wall. Experiments were conducted in a hypersonic wind tunnel using a 5-degree half-angle cone with four flare compression-surface angles. The free stream Mach number was about 14.5 at the model tip. The free stream was slightly divergent. A number of peripheral problems were investigated; among these are the effects on the flow of: the slightly divergent freestream, minute tip-bluntness, slip-flow, and shock viscous-layer interactions. All of these factors influenced the flow upstream of separation-interaction. A qualitative analysis indicates that the separated regions were significantly altered by the effects of the slight free-stream non-uniformity. Nevertheless, surface-pressure distributions for three separation-interaction regions are still correlated by parameters developed from a simplified, semi-empirical, hypersonic, laminar, free-interaction analysis. The experimental observation techniques included detailed surface pressure measurements, pitot surveys of the separated flow (which were converted into velocity and Mach number profiles), Tempilag fluid-flow studies and the use of pure-carbon tufts. The flow-visualization techniques are an advance in the experimental art because they are applicable at high surface temperatures, i.e., temperatures at 1460 R and perhaps beyond. However, these techniques were not fully exploited in the investigation. (Author).