Preheat oven to 375F degrees. Clean the Cornish Hens; sprinkle insides with salt. Dry hens thoroughly and place them breast side down on a rack in a roasting pan. Also place livers on rack. Mix the soy sauce and butter together and brush the hens with half the mixture. Place in oven. Baste every 10 minutes.
Halfway through the estimated roasting time, remove the livers, turn hens to other side and brush. Continue basting.
Ten minutes before the end of the estimated roasting time, when hens are fairly brown, glaze with 1/4 cup of apricot/pineapple jam, being careful not to spill any directly on the roasting pan. Do not allow the drippings to cook with the jam longer than 10 minutes or sauce will become burned. After 10 minutes, remove hens to platter.