* ISS, Glass Lewis oppose parts of proposed compensation
* Swiss firms' shareholders get binding vote on bosses' pay
* Vote to take place at AGM on April 28 (Adds ISS recommendation)
By Joshua Franklin
ZURICH, April 18 (Reuters) - Credit Suisse has failed to completely quash a shareholder revolt over payouts to the bank's senior managers, even after offering to cut bonuses for top management by 40 percent and a pay freeze for its board of directors.
The Swiss bank made the concessions last week to head off shareholder criticism of its pay plans, which included bonuses of 78 million Swiss francs ($78 million) to top executives and higher pay for the board despite a 2.7 billion-franc net loss last year.
Proxy advisor Institutional Shareholder Services (ISS)softened its stance by asking shareholders of the bank to vote in favour of the board of directors' pay and the long-term variable pay for the executive committee.
ISS said it was still against the proposed short-term variable pay for the executive committee and the overall pay proposals.
Shareholder advisory service Glass Lewis said the concessions were "too little too late". It urged shareholders to reject the maximum amount of compensation for the board of directors, but advised them to support the proposed bonuses for Credit Suisse's executive board.
Shareholders in Switzerland have veto power over management and board pay following a 2013 "fat cat" referendum on the issue. If Credit Suisse shareholders reject the plan, it would be the first use of the Swiss veto at a leading company. Shareholders will vote at the bank's annual general meeting on April 28.
Investors have become much more vocal in opposing big increases in executive pay and bonuses when a company has not performed strongly.
American International Group Inc's CEO Peter Hancock will not get a cash bonus for last year after the company's poor performance roiled shareholders. BP cut CEO Bob Dudley's 2016 pay package by 40 percent after shareholders opposed the oil company's pay plans.
Credit Suisse has now published those amendments to its Annual General Meeting agenda.
If shareholders vote against the compensation, Credit Suisse's board of directors may submit a new proposal to an extraordinary general meeting or to the next AGM, according to Credit Suisse's articles of association.
ISS and Glass Lewis represent 15-20 percent and 10 percent of Credit Suisse shareholders respectively, according to an estimate from Swiss shareholders' advisory firm Ethos.
Despite Credit Suisse's concessions, Ethos still opposes the pay proposals, saying they remain too generous in light of the bank's 2016 losses.
Some investors are throwing their weight behind the pay plan, including Norway's sovereign wealth fund. The fund, which owns about 5 percent of Credit Suisse, said the bonus cut demonstrated "the board has listened to shareholder concerns".
Overall, CEO Tidjane Thiam's compensation will drop by 4.67 million francs through the bonus cut, although his 2016 compensation will fall only to 10.24 million francs from 11.9 million because the bulk of the reduction comes from 2017 long-term payments.
The pay packet still makes Thiam one of Europe's highest-paid bank bosses.
Credit Suisse's board will get compensation of 12 million francs, from 12.5 million previously, under the proposals.
Since taking over as CEO in mid-2015, Thiam has shifted the bank's focus towards wealth management while shrinking Credit Suisse's investment bank.
The costly restructuring and heavy penalties for selling toxic mortgage debt in the run-up to the financial crisis meant a second straight full-year loss for Credit Suisse.
($1 = 1.0033 Swiss francs)
Additional reporting by Oliver Hirt and John Miller; Editing by Michael Shields and Jane Merriman