An algorithm for microprocessor-controlled seismographic recorders is described which reliably detects major phases from earthquakes more than 3° from the sensor but rejects noise events and most earthquakes closer than 3°. Unusually large earthquakes within 3° also are detected. The algorithm is applicable to field studies using triggered seismographs to record teleseismic P waves, to worldwide network automation, and to scanning records for teleseisms. It uses two band-pass filtered data streams evolved from a single short-period vertical-component seismometer to differentiate (low-frequency) teleseisms from other signals; the low-frequency band (0.5 to 2.0 Hz) declares “triggers” while the high-frequency band (3.0 to 8.0 Hz) inhibits any of these triggers generated by broadband signals such as local earthquakes. Locally generated noise is usually high frequency and does not excite the low-frequency band. A 16-bit fixed-word-length implementation of this algorithm detected 82 per cent of good P phases (readable to ±0.25 sec) occurring more than 20° from the seismograph, and 50 per cent of earthquakes between 3° and 20°, in a test data set comprising 23 hr of data in 93 segments. The same implementation of the algorithm rejected most noise and 91 per cent of earthquakes within 3° of the seismograph.