The degree of competition in science, it is argued, was underemphasized in the past but more recently has been overemphasized. Data from a study of bio-medical scientists is used to show that science is not uniformly competitive or non-competitive. The degree of competition that a scientist feels in his daily work varies with his specific location in the age and stratification structures of science. Competition is shown, further, to result in an increase of secretive behavior among scientists, and it is argued that secrecy may represent a cost for science and, ultimately, for society.