With the development of programmable data plane (PDP), in-band network telemetry (INT) has become a promising network monitoring technique to visualize network operations in a fine-grained and real-time way. In this work, to better balance the tradeoff between INT overheads and monitoring accuracy, we design and optimize an information-sensitive INT system (namely, P4InfoSen-INT), which makes each PDP switch decide locally whether and what type(s) of telemetry data should be inserted in a packet based on the “information content” of the data, and implement it in P4-based PDP switches. We first realize the basic principle of P4InfoSen-INT with P4 programs. Then, we propose algorithms to estimate the information content of telemetry data accurately in a dynamic network and optimize the tradeoff between INT overheads and monitoring accuracy. Finally, we further optimize the implementation of P4InfoSen-INT by proposing table merging to reduce stage occupation in each switch. Experimental results verify that our proposed P4InfoSen-INT can balance the tradeoff between INT overheads and monitoring accuracy better than existing benchmarks.