Combine first 8 ingredients in a medium bowl, stirring well.
Spread 1/4 cup tuna mixture on each of 4 slices of bread. Top evenly with cheese slices, carrot, cucumber, and lettuce. Top with remaining bread slices, and cut in half.
Tip: Eating tuna once or twice a week poses no health risk for healthy adults. However, avoid eating it more frequently because tuna--both canned and fresh--contains high levels of mercury that can cause chronic fatigue and memory loss in adults. Mercury can also harm an unborn child's developing nervous system. If you are pregnant, considering pregnancy, or nursing, it's best to avoid tuna.
Unlike most, I AM a mayo fan, so I followed recipe, but it was WAY to "wet", so I mixed in the carrots and added chopped green pepper to thicken up...not too bad. Cut back on mayo or add additional veggies. Didn't have fresh dill, so used dried dill weed. Placed on bread and toasted w/ cheese on top.
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