Wash, then peel cucumber. Dry with a paper towel to remove dampness.
Slice into thin, even pieces.
Carefully spread room temperature butter onto one slice of bread.
Place cream cheese into a small bowl and stir with a fork to soften. Spread onto the second slice of bread.
Layer cucumber slices over the cream cheese then sprinkle a little dill on top. Top with buttered bread slice.
With a long knife, carefully cut off crusts from each side of sandwich. Cut in half, diagonally, and if desired again into fourths.
Serve immediately, or wrap with plastic wrap and chill until ready to serve.