This paper presents SoftRate, a wireless bit rate adaptation protocol that is responsive to rapidly varying channel conditions. Unlike previous work that uses either frame receptions or signal-to-noise ratio (SNR) estimates to select bit rates, SoftRate uses confidence information calculated by the physical layer and exported to higher layers via the SoftPHY interface to estimate the prevailing channel bit error rate (BER). Senders use this BER estimate, calculated over each received packet (even when the packet has no bit errors), to pick good bit rates. SoftRate's novel BER computation works across different wireless environments and hardware without requiring any retraining. SoftRate also uses abrupt changes in the BER estimate to identify interference, enabling it to reduce the bit rate only in response to channel errors caused by attenuation or fading. Our experiments conducted using a software radio prototype show that SoftRate achieves 2X higher throughput than popular frame-level protocols such as SampleRate and RRAA. It also achieves 20% more throughput than an SNR-based protocol trained on the operating environment, and up to 4X higher throughput than an untrained SNR-based protocol. The throughput gains using SoftRate stem from its ability to react to channel variations within a single packet-time and its robustness to collision losses.