This course is designed to unveil physics to students in introductory physics laboratory by teaching them to discover it on their own. The University Versatile Eclectic Introductory Laboratory (UNVEIL) course combines several of the most effective current laboratory teaching methods into one course designed to (1) meet the needs of both premedical students and science/engineering students who are mixed together in sections of lab; (2) use technology both to teach physics and to introduce students to professional-level equipment; (3) employ successful pedagogy to maximize physics understanding. Computers and self-discovery pedagogy allow for a versatile laboratory where students in the same room can perform different experiments. UNVEIL combines Socratic guidance, self-discovery, computer technology, and modeling methods to create a more effective lab environment. Equipment and software have been selected that can largely be used by both groups of students, with each group performing some specifically tailored experiments. Newly developed, versatile physics laboratory equipment, along with Power Macs, LabVIEW data acquisition software, Mathematica, and other software are used. The laboratory course is one in which students, armed with the laboratory manual, can select appropriate equipment and design an experiment (with Socratic guidance from the instructor and TAs) to examine the subject. With the computer, students acquire data or enter data acquired manually, plot graphs, and look at computer modeling of physical phenomena.