The Mediterranean diet is rich in fruit and vegetables
Adopting just a couple of elements of the Mediterranean diet could cut the risk of cancer by 12%, say scientists.
A study of 26,000 Greek people found just using more olive oil alone cut the risk by 9%.
The diet, reports the British Journal of Cancer, also includes higher amounts of fruits, vegetables, cereals, and less red meat.
A separate study found adding broccoli to meals might help men vulnerable to prostate cancer cut their risk.
The Mediterranean diet came under scrutiny after researchers noticed lower rates of illnesses such as heart disease in countries such as Spain and Greece.
They noticed that people living there generally ate more vegetables and fish, less red meat, cooked in olive oil and drank moderate amounts of alcohol.
The latest study is one of the largest yet to look at the potential impact on cancer of the various parts of this diet.
Researchers from Harvard University persuaded thousands of Greek people of various ages to record their food intake over an eight-year-period.
Broccoli may help ward off prostate cancer
Their adherence to the Mediterranean diet was ranked using a scoring system, and the group with the worst score compared with those who followed a couple of aspects of the diet, and those who followed it the most closely.
The biggest effect they found - a 9% reduction in risk - was achieved simply by eating more "unsaturated" fats such as olive oil.
But just two changes - eating less red meat, and more peas, beans and lentils, cut the risk of cancer by 12%.
Dr Dimitrios Trichopoulos, who led the study, said: "Adjusting one's overall dietary habits towards the traditional Mediterranean pattern had an important effect."
Sara Hiom, from Cancer Research UK, said the research highlighted the importance of a healthy balanced diet.
"It shows there are a number of things you can do, and there is no one 'superfood' that can stop you developing the disease."
The other study suggesting that food had the power to prevent cancer came from the Institute of Food Research in Norwich.
Scientists compared the effects of adding 400 grams of broccoli or peas a week to the diet of men at high risk of prostate cancer - and in the case of broccoli found differences in the activity of genes in the prostate which other studies have linked to cancer.
Their findings raised the possibility that broccoli, or other "cruciferous" vegetables, such as cauliflower and Brussels sprouts, could help prevent or slow down the disease, particularly if the man had a particular gene variant - GSTM1.
Professor Richard Mithen, who led the research, published in the Public Library of Science journal, said: "Eating two or three portions of cruciferous vegetables per week, and maybe a few more if you lack the GSTM1 gene - should be encouraged."
Professor Karol Sikora, medical director of CancerPartnersUK, said the study was the first time in a properly controlled clinical trial that broccoli had been shown to change the expression of specific genes in the prostate gland.
"Although the observation period was too short and the numbers too small to show that the incidence of cancer actually fell, it is the first clear demonstration that broccoli and presumably other cruciferous vegetables may well reduce cancer risk."