Patents lead to ex-post dead-weight losses arising from a non-competitive market structure for the invention. Many have argued that introducing independent invention as a defense (IID) to patent infringement can increase social welfare by decreasing such dead-weight losses at the price of a modest decrease in the number of inventions. This paper considers the effects of IID in a setting where R&D firms have incomplete information about their rivals. Four main results follow under incomplete information: (i) Fewer things are invented under an IID regime, (ii) IID's effects on welfare are ambiguous, (iii) IID is more likely to increase welfare if gains from competition in the product market are high, and (iv) determining precise conditions under which IID performs better than the current regime requires access to data which is extremely hard to find and quantify.