Some banks and building societies have been edging up rates for new savers. BM Savings has raised the rate on its easy-access Online Extra to a top 1.6% before tax (1.28% after tax).
It actually gives new savers a small positive return now that inflation has fallen to 1.2% a year. The rate includes a bonus for the first 12 months after which it drops to 0.5% (0.4%).
The top deal without a bonus is 1.3% (1.04%) from Virgin Money.
On fixed rate deals you can earn 1.9% (1.52%) on the new bond, launched on Monday, from National Counties Building Society, fixed until 29 June next year.
Find the best Cash Isa or savings account for you
And those looking for tax-free cash Isas can earn 1.6% with BM Savings Isa Extra Issue 12, launched last week. Once again the rate includes a bonus for the first year and you can transfer your existing cash Isas into the account.
The best deal with no short-term bonus to boost the headline rate comes from National Savings and Investments at 1.5%, but you cannot transfer your cash Isas from other providers into the account.
The top deals with no bonus which does accept transfers come from Teachers Building Society and Sainsbury's Bank, at 1.45%. If you have built up £30,000 or more in your cash Isas, Barclays pays a slightly higher 1.49%, with no initial bonus.
Top fixed-rate cash Isas include Post Office at 1.7% and Tesco Bank at 1.65% for one year and Virgin Money at 2.1% for two years.
This article was written for our sister website Money Observer