Some languages, like English, require overt surface subjects, while others, like Italian and Spanish, allow "null" subjects. How does the young child determine whether or not her language allows null subjects? Modern parameter-setting theory has proposed a solution, in which the child begins acquisition with the null subject parameter set for either the English-like value or the Italian-like value. Incoming data, or the absence thereof, force a resetting of the parameter if the original value was incorrect. This paper argues that the single-value solution cannot work, no matter which value is chosen as the initial one, because of inherent limitations in the child's parser, and because of the presence of misleading input. An alternative dual-value solution is proposed, in which the child begins acquisition with both values available, and uses theory-confirmation procedures to decide which value is best supported by the available data.