Combine the cream cheese, sour cream or mayo, chopped dill, and salt in a bowl, stirring until the mixture is smooth and fully blended.
Spread the mixture onto one side of each bread slice using a small spatula or butter knife.
Layer cucumber slices onto half of the bread slices, overlapping them slightly.
Top with the remaining bread slices, spread side down, and press gently to secure the sandwiches.
Remove the crusts with a serrated knife and cut each sandwich into four small rectangles or triangles.
Arrange the sandwiches on a serving platter and garnish with additional dill or cucumber slices if desired.
