Doctors could seek the help of trained co-ordinators while obtaining consent for organ donation from bereaved families.
A study in John Radcliffe Hospital, UK also suggested organ donation should not be raised when informing families of the death of the patient.
The Oxford hospital study comes in the backdrop of previous findings that show that as many as four in 10 relatives deny consent.
The Radcliffe team reviewed 20 previous studies on organ donation, the British Medical Journal reported.
Some of these looked at having the conversation about consent at a different time to announcing the death of the patient to the family.
These showed "decoupling" the conversations was up to three times more likely to result in consent been given. It made little difference if the donation discussion was held before or after death.
Another study showed that seven in 10 requests made jointly by the doctor and hospital's transplant coordinator were successful.
Lead researcher Dr Duncan Young said: "I think these are invaluable lessons for hospitals.
"All too often officials will get involved in conversations about organ donation when informing the relative their loved one has died. But just having that time, even just a little time, to accept things seems to make a difference.
"I think the importance of having both a coordinator and doctor is to do with doctors not having the social skills to discuss this in the best manner.
"Many doctors will not necessarily deal with that many donor cases so they are not used to it. Whereas having a trained coordinator makes a big difference.
"However, the doctor is still important as they are likely to be a familiar face to the family."
Transplant coordinators are specially-trained staff who oversee organ donor issues at hospitals. They are not yet employed routinely across the NHS and instead tend to be focused on the biggest centres.
Sally Johnson, of NHS Blood and Transplant, the official authority that oversees transplants in the NHS, said the findings reinforce the need for the positions and said she hoped more hospitals would look to use them.
"We hope that this research will help them to understand the benefits of involving an expert donor transplant co-coordinator at the right time."
Transplant officials said the findings should inform hospital practice.
The refusing of consent by families, even when a person is on the donor register, is a major problem for the NHS. There are 16m people on the register in the UK - a record number.
But three people a day die on average waiting for an organ.