Beat butter with dill, lemon zest, lemon juice and pepper until smooth and spreadable. Keep the salmon refrigerated while preparing the bread.
Spread one face of every rye slice with a thin even layer of flavored butter, taking it to the corners.
Divide salmon equally among eight slices, laying the fish in a flat layer and trimming overhangs to fill any gaps. Close with the remaining slices, buttered sides inward.
Cover and refrigerate the sandwiches for 15 minutes to firm the butter slightly. Trim crusts with a sharp serrated knife without pressing down hard.
Cut each sandwich into three equal fingers for 24 pieces. Serve two per portion and keep covered in the refrigerator until serving the same day.