How To End Illegal Immigration

Around one in thirty people in the US are there without proper documentation. They are illegal immigrants, from Mexico, Honduras, Guatemala and other places, drawn to the high wages and low unemployment in the US. Most other developed countries have lower levels of illegal immigration, some much lower. More interestingly still, some of these are near even poorer countries, have higher wages, and lower levels of of unemployment. Why do these countries attract so many fewer illegal immigrants than the US? What is it about Switzerland or Norway's policies that mean they have so many fewer illegals? In other words, will building a wall keep the illegal immigrants out, or is there a better way?