Trim the fillets of any fat and sinew. Season with salt and pepper and toss in olive oil. Panfry over moderate heat for about 10 minutes for rare (longer until cooked the way you like a steak), turning frequently.
Remove from the pan, transfer to a plate, cover loosely with foil and rest for 6 minutes.
To serve, slice on the diagonal.
Good with the classic venison accompaniment—3/4 cup melted red currant jelly mixed with a tablespoon of wholegrain mustard, the zest and juice of an orange and chopped parsley.