The ideal of scientific openness, i.e., the idea that scientific information should be freely accessible to interested parties, is strongly supported throughout the scientific community. At the same time, however, this ideal does not appear to be absolute in the everyday practice of science. In order to get the credit for new scientific advances, scientists often keep information to themselves. Also, it is common practice to withhold information obtained in commissioned research when the scientist has agreed with his or her employer to do so. The secrecy may be intended forever, as in the military area, but also temporarily until a patent application has been made. The paper explores to what extent such secrecy is undesirable, as seems to be suggested by the ideal of scientific openness.