If satellite coverage (global or partial) of the Earth surface is necessary, continuous coverage may not be justified by the purpose of orbital constellation and is not mandatory. Whereas the providing of continuous coverage is connected with the application of rather big number of satellites, periodic coverage is direct way of minimizing of necessary number of satellites and, therefore, decreasing the costs of satellites launching. The traditional criterion of the quality of the satellite constellations at periodic coverage is revisit time calculated under the assumption that the value of satellite swath is fixed. But in many important applications the revisit time value could be a priori given proceeding from specific requirements to the satellite constellation. There is a good chance in this case to reduce additionally the cost of the observations minimizing satellite swath. The description of mathematical problem of the satellite swath minimizing as well as general solution of this problem, are presented in the paper. High emphasis is placed on different methods of optimal satellite design for periodic coverage with minimal satellite swath. Possible combinations of satellite orbit parameters and Earth coverage characteristics are reduced to some typical cases illustrated by numerical data. The optimal orbits (altitude and inclination) for low-cost observation (in terms of minimal satellite swath) are described. The suggested methods are compared with well-known methods of low-cost Earth observation from space. Copyright IAF/IAA. All rights reserved.