A novel seal is provided along with a valve for implementing the seal in the form of a hemostatic catheterization valve. A pressure-sensing form of the hemostatic valve is also provided. The novel seal includes a pair of cooperating conical gaskets divided through their apexes into a plurality of edge-abutting semi-conical flaps. The seals are angularly fixed in orientation relative to each other using registering structures such as complementary tabs and sockets. More specifically, the seams where the semi-conical flaps abut are angularly off-set between the two conical gaskets by a predetermined amount.
