We characterize the effect of rubidium ions on water-ice nanoislands in terms of area, fractal dimension, and apparent height by low-temperature scanning tunneling microscopy. Water nanoislands on the pristine Cu(111) surface are compared to those at similar coverage on a Rb+ pre-covered Cu(111) surface to reveal the structure-giving effect of Rb+. The presence of Rb+ induces changes in the island shape, and hence, the water network, without affecting the nanoisland volume. The broad area distribution shifts to larger values while the height decreases from three bilayers to one or two bilayers. The nanoislands on the Rb+ pre-covered surface are also more compact, reflected in a shift in the fractal dimension distribution. We relate the changes to a weakening of the hydrogen-bond network by Rb+.