Despite much research on the ecological impacts of urbanization, we still do not know what development patterns are most effective in supporting ecological function. In particular, it is as yet unclear if compact urban forms are ecologically more favourable than dispersed forms. Using historical data from the city of Geneva in Switzerland, we present results on its growth from 1841 to 2005, or for 165 years. We first show that the main street orientations have been maintained since the initiation of the city, which implies that the Shannon-Gibbs orientation entropy has been essentially constant during this period. We also show that the length-size distributions of the streets follow power laws and that the length entropy has, in contrast to the orientation entropy, gradually increased during the 165-year evolution of the city. This means that the maximum length and the average length of the street network has increased as the network has expanded. This study suggests that the city of Geneva has grown through two processes: expansion and densification. In Geneva, expansion has dominated during the entire period, but there has also been densification, particularly in the second half of the period. City expansion means that the land used for human activities increases over time. The urban area covered by Geneva increased from about 0.6 km2 in 1841 to about 16 km2 today, so that the area covered by fields and woodlands and available to plants and animals has reduced by more than 15 km2 during this period. Similarly, densification normally (but not always) implies that the green areas available for plants and animal inside the city reduce in size. Densification results in less average human-travel distances, less fuel consumption for transportation, and less land being urbanized; it is also favourable to certain aspects of the ecosystem. Densification may thus be a viable planning scenario for the future growth of many cities, in Switzerland and elsewhere. However, expansion appears to favour other aspects of the ecosystem, and further studies are needed to assess ecologically the overall pros and cons of city densification versus expansion.