Network measurement is essential for efficient network management and operations. In-band network telemetry (INT) offers fine-grained per-device per-packet information which could provide full-visibility for networks. However, the existing solutions fall short in achieving high accuracy, generality, and low overhead simultaneously. To address this limitation, we introduce OffsetINT to meet these three criteria. The key idea of OffsetINT is to use minimal bits to carry collected states during monitoring, which is based on our observation that the value of telemetry states are usually very close (e.g., the time of adjacent arrival packets) or small (e.g., only a few tens of microseconds for processing latency) for most of the time in real networks. Instead of embedding complete values of state in packets, OffsetINT optimizes bit usage by encoding an offset (using fewer bits), which is carried in-band by passing packets to the end-hosts for recovery and analysis. We theoretically derive the bounds of bandwidth mitigation for OffsetINT. We have implemented OffsetINT in both P4 hardware switches (with Intel Tofino ASIC) and BMv2. Expensive evaluation results show that OffsetINT can achieve an accuracy of up to 100% compared to the original INT while reducing INT bandwidth by up to 48%.