A special thinned array structure, termed Minimum Redundancy Array (MRA), is proposed and investigated for interference cancellation. This array structure has been proved in the past to have advantages in direction finding application. Exclusive attention is given to the Minimum Noise Variance (MNV) performance of MRAs operating in a multiple narrow-band interference environment which is the most suitable for applications wherein the desired signal can be assumed absent during weight adaptation, as for example in radar. Particular attention is focused on the single and two-interference cases. The closed-form equation for the optimal signal-to-interference plus noise ratio is obtained for both array structures as a function of the number of array elements, the direction of the interferences and their power to noise ratio. Performance comparison is done numerically. A recursive formula for the inverse of the correlation matrix is found and used to evaluate the performance of the arrays operating under more than two interferences. It is also shown that MRA almost always outperform URA when they are used as interference cancellers. Simulation results supplement this conclusion.