Design method for band-stop filters (BSFs) that suppress a requested number of spurious bandstops and reduce ripples in the passbands below ~1 dB is proposed. BSF is designed in a form of a cascade of cells, each consisting of steps of equal electrical length, where the number of steps is used to control the number of suppressed spurious bandstops. Analytical formulas are developed that enable initial design of BSF for a given central frequency, depth, and bandwidth of the stopband. Varying the minimum characteristic impedances of initial cells, through an optimization using circuit simulation, the ripples in passbands are reduced below ~1 dB. Using the proposed theory, three filters in microstrip technology, with suppression of 3, 5, and 7 spurious stopbands respectively, were designed, fabricated, and measured. Good agreement between simulated and measured results has been observed. The proposed design can be recommended for filters having broad stop bandwidths, between 40 and 100%.