A new perspective on cognitive radio is presented for the case where the primary transmission is in uncoded analog form. The basic idea is to exploit signal-to-noise ratio margins in primary receivers, and to optimize cognitive signals by appropriately shaping their spectrum. It is shown that coexistence of primary and cognitive users is possible even without message-sharing, and furthermore, the cognitive user is no longer interference-limited, but can always transmit at its full available power thus achieving logarithmic growth of its information rate as its average power constraint grows large.