We conducted three studies with contemporary music composers at IRCAM. We found that even highly computer-literate composers use an iterative process that begins with expressing musical ideas on paper, followed by active parallel exploration on paper and in software, prior to final execution of their ideas as an original score. We conducted a participatory design study that focused on the creative exploration phase, to design tools that help composers better integrate their paper-based and electronic activities. We then developed InkSplorer as a technology probe that connects users' hand-written gestures on paper to Max/MSP and OpenMusic. Composers appropriated InkSplorer according to their preferred composition styles, emphasizing its ability to help them quickly explore musical ideas on paper as they interact with the computer. We conclude with recommendations for designing interactive paper tools that support the creative process, letting users explore musical ideas both on paper and electronically.