British Basketball has been awarded £7m by UK Sport after appealing against a decision to cut its funding.
Wheelchair fencing has also been awarded funding from the body for an initial 12 months.
UK Sport say the sports must fulfil "strict performance criteria" for money in the following three years, while beach volleyball gets an increase.
Wheelchair fencing, which like basketball saw its funding reduced to zero, has been awarded just over £1m, while women's beach volleyball has had its funding increased from £386,753 to £514,000.
UK Sport said the three sports had presented "new and compelling evidence to demonstrate their case for revised funding for the Rio cycle".
They added that the awards for basketball and wheelchair fencing would be "on a one-year conditional basis with the following three years' funding released only on the fulfilment of strict performance criteria".
In 2006, British Basketball was awarded £8.6m through to London 2012, but that was cut altogether when for Olympic sports in the lead-up to Rio 2016.
The decision prompted Team GB and Chicago Bulls star Luol Deng to write to Prime Minister David Cameron demanding that the funding was restored.
UK Sport also added that "it has not received any formal appeals to Sport Resolutions UK on its Rio cycle investments" from handball, table tennis, wrestling and volleyball (sitting, men's beach and indoor), which will not receive support for Rio 2016.