Only three out of 17 water firms in England and Wales have passed the latest review by regulator Ofwat.
All firms had to submit plans to cut bills for millions of consumers over the 2020-25 period, while reducing leaks and helping vulnerable customers.
Most failed to meet the regulator's requirements.
But plans from Severn Trent, United Utilities and South West Water were approved. The rest have been told to go back to the drawing board.
"In the coming months, the remaining water companies will have to strengthen their plans so they too deliver for customers," Ofwat said.
"Four companies - Affinity Water, Hafren Dyfrdwy, Thames Water and Southern Water - have the most work to do in order to meet the tough challenges Ofwat has laid down for the sector."
Severn Trent has pledged to cut customers' bills by an average of £18 a year in real terms by the 2024-25 financial year as part of its business plan.
United Utilities has proposed a £43 cut, while South West Water's planned cut is £73.
More for less
Ofwat chief executive Rachel Fletcher said: "We have challenged all water companies to deliver more for less for customers over the next five years.
"Three companies have already stepped up to the mark with high-quality plans and stretching commitments to customers for the next five years.
"The rest of the sector now needs to meet this high standard so that customers across the country get better and more efficient services."
The remaining 14 firms must submit revised plans by 1 April. Ofwat will say what it thinks of them in July, while its final word on the matter will come in December.
As well as price cuts, Ofwat wants to see leaks reduced by 15%, which it says would save enough water for three months' worth of daily showers for everyone in England and Wales.
It also wants more help for customers struggling to pay their bills, with forecasts suggesting there could be 1.5 million of them by 2024-25.
Thames Water executive Steve Robertson said the company was "disappointed" with Ofwat's assessment of its £11.7bn five-year business plan, which he said tackled leakage and pollution while keeping average bills "flat".
He added: "We remain committed to our forward-looking plan, which prioritises investment over everything else - including shareholder dividends.
"We'll now study the feedback in detail and look forward to engaging constructively with Ofwat throughout this process."