With Melbourne's rental market getting particularly tight, landlords can afford to be particular with their chosen tenants beyond their usual exacting standards. As of May 2016, only 1.6 per cent of houses in Melbourne are vacant, and vacancy rates are low across all areas of the city.

According to Tenants Union of Victoria spokeswoman Yaelle Caspi, discrimination is widespread among landlords, but it is hard to prevent and difficult to prove. There are also gender equality issues as some women with reasonable incomes also found it hard to find a house to rent. In general, men are perceived to be more reliable earners.

"Young people and single parents are known as the least preferred tenants," she said. "Large families and people with disabilities, as well as Aboriginal people and people from culturally and linguistically diverse backgrounds also report discrimination."

According to the Equal Opportunity Act, landlords should not discriminate against families with children, but it sometimes happens when there are several applications.

"There are some owners who will say, 'I'd rather have a dog in the property than three young kids,' because of the potential damage that a child can do," said Biggin and Scott Brighton's Elizabeth Lopez. "Often, single parents are so grateful to be given that opportunity because they have struggled that they make wonderful tenants."

In general, apartment landlords prefer professional couples over families with children.

"The wear and tear would probably be lower with a professional couple in an apartment whereas landlords who own small houses or townhouses are already in the mindset that a family is going to apply because it's more family-friendly," said Beller's Luke Spence.