Fixed-rate deals from new challenger banks continue to edge up. FirstSave now pays 2.12 per cent before tax (1.7 per cent after tax), fixed for one year. The new deal puts it just behind the top payer, Shawbrook Bank, at 2.15 per cent (1.72 per cent after tax).Other good deals for one year include Charter Savings Bank at 2.07 per cent (1.66 per cent), along with RCI Bank at 2.06 per cent (1.65 per cent).Shawbrook also pays top rates for longer-term deals, at 2.35 per cent (1.88 per cent) for 18 months and 2.45 per cent (1.96 per cent) for two years.On easy-access taxable accounts the best rate is still at 1.65 per cent (1.32 per cent) from RCI Bank Freedom Account. With this bank you are not covered by the UK compensation scheme. If the bank goes bust you claim from the European scheme, where the maximum amount is €100,000 (around £70,000).Cash IsasThe next best rate is Virgin Money Defined Access Saver at 1.51 per cent (1.21 per cent), but the bank restricts you to making three withdrawals a year at most from your account.On tax-free cash Isas, top deal with no bonus and no withdrawal restrictions comes from Coventry Building Society at 1.5 per cent. You can earn slightly more with Virgin Money Defined Access Isa rate at 1.56 per cent, but it limits you to making three withdrawals a year.Post Office Online Cash Isa pays 1.51 per cent, but the rate includes a 0.86 percentage point bonus for the first 12 months, after which the rate drops to 0.65 per cent.The best fixed-rate cash Isa deals come from Shawbrook Bank at 1.95 per cent fixed for one year, followed by Virgin Money at 1.71 per cent.For two years Coventry Building Society pays 2.05 per cent fixed until 30 November 2017. Alternatively AA Savings, where the deposit taker is Bank of Ireland, pays 2.01 per cent, while Shawbrook Bank, Principality Building Society and Virgin Money all offer 2 per cent.Yorkshire Building Society's new fixed rate cash Isa fixed at 2.3 per cent until December 2018 is the top three-year deal. It's also available from its offshoots Barnsley, Chelsea and Norwich & Peterborough building societies.All accept transfers from other providers.