Energy Efficiency Is An Important Design Criterion For The Development Of Sensor Networking Protocols Involving Data Dissemination And Gathering. In-network Processing Of Sensor Data, Aggregation, Transmission Power Control In Radios, And Periodic Cycling Of Node Wake-up Schedules Are Some Techniques That Have Been Roposed In The Sensor Networking Literature For Achieving Energy Efficiency. Owing To The Broadcast Nature Of The Wireless Channel Many Nodes In The Vicinity Of A Sender Node May Overhear Its Packet Transmissions Even If They Are Not The Intended Reci Ients Of These Transmissions. Reception Of These Transmissions Can Result In Unnecessary Expenditure Of Battery Energy Of The Recipients. In This Paper, We Investigate The Impact Of Overhearing Transmissions On Total Energy Costs During Data Gathering And Dissemination And Attempt To Minimize Them Systematically. We Model The Minimum Energy Data Gathering Problem As A Directed Minimum Energy Spanning Tree Problem Where The Energy Cost Of Each Edge In The Wireless Connectivity Graph Is Augmented By The Overhearing Cost Of The Corresponding Transmission. We Observe That In Dense Sensor Networks, Overhearing Costs Constitute A Significant Fraction Of The Total Energy Cost And That Computing The Minimum Spanning Tree On The Augmented Cost Metric Results In Energy Savings, Especially In Networks With Non-uniform S Atial Node Distribution. We Also Study The Impact Of This New Metric On The Well Known Energy-efficient Dissemination (also Called Broadcasting) Algorithms For Multihop Wireless Networks. We Show Via Simulation That Through This Augmented Cost Metric, Gains In Energy Efficiency Of 10%or More Are Ossible Without Additional Hardware And Minimal Additional Complexity. Sponsored By Acm And Ieee. Includes Bibliographical References And Author Index. Also Available Via The World Wide Web.