Put the jointed poussins in a large roasting tin and season all over with salt and pepper. Mix together the lime rind and juice, Cajun spice and 1 tablespoon of the olive oil and use to brush over the poussin pieces. Cook on a hot barbecue, turning occasionally, for 25 minutes or until golden in places and cooked through.
Meanwhile, put the sweetcorn in a mixing bowl with the chilli, cucumber and the remaining olive oil. Toss together well and serve with the cooked poussin pieces.