A wireless handheld device comprises an internal antenna system that operates in first and second non-overlapping frequency bands with respective bandwidths. The antenna system includes: a ground plane; first and second antenna elements connected to a common input/output port, wherein a bandwidth of each of the antenna elements is less than at least one of the first and second operating frequency bandwidths and less than a frequency bandwidth for the antenna system; a combining structure to couple first and second signal transmission paths from the antenna elements to the common input/output port; and a phase shifting element on the first signal transmission path that imparts a phase delay to signals on the first signal transmission path. The phase delay minimizes a sum of reflection coefficients of the antenna elements to cause the frequency bandwidth for the antenna system to include at least the first and second operating frequency bands.