This paper reports new observations of pulsars B0943+10 and B1822−09 carried out with the Arecibo Observatory and the Giant Metrewave Radio Telescope, respectively. Both stars exhibit two stable emission modes. We report the discovery in B0943+10 of a highly linearly polarized ‘precursor’ (PC) component that occurs primarily in only one mode. This emission feature closely resembles B1822−09's PC which also occurs brightly in only one mode. B0943+10's other mode is well known for its highly regular drifting subpulses that are apparently produced by a rotating ‘carousel’ system of 20 ‘beamlets.’ Similarly, B1822−09 exhibits subpulse-modulation behaviour only in the mode where its PC is absent. We survey our 18 h of B0943+10 observations and find that the ‘sideband’-modulation features, from which the carousel-rotation time can be directly determined, occur rarely – less than 5 per cent of the time – but always indicating 20 ‘beamlets’. We present an analysis of B1822−09's modal modulation characteristics at 325 MHz and compare them in detail with B0943+10. The pulsar never seems to null, and we find a 43-rotation-period <it>P</it><inf>3</inf> feature in the star's ‘Q’ mode that modulates the interpulse (IP) as well as the conal features in the main pulse (MP). We conclude that B1822−09 must have a nearly orthogonal geometry and that its carousel circulation time is long compared to the modal subsequences available in our observations, and the MP/IP separation is almost exactly 180°. We conclude the PCs for both stars are incompatible with core–cone emission. We assess the interesting suggestion by Dyks et al. that downward-going radiation produces B1822−09's PC emission.
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