* New rule takes effect in 2019
* Covered bonds given effective exemption
* Less strict treatment of credit default swaps
(Recasts with more detail, background)
LONDON, April 15 (Reuters) - Global regulators have eased a new rule limiting how much business a bank can undertake with a single customer, as they try to minimise the risk of fallout from a counterparty going bust without imposing excessive burdens on financial firms.
Regulators want to avoid the damage to financial stability an insolvency can wreak, as seen with the collapse of U.S. bank Lehman Brothers in 2008 which led to taxpayers bailing out several lenders.
"In cases where the bank's counterparty is another bank, large exposure limits will directly contribute towards the reduction of system-wide contagion risk," the Basel Committee of banking regulators said in a statement on Tuesday.
The committee, made up of banking supervisors from nearly 30 countries, published the final version of a new rule that will take effect in 2019, bumping up compliance costs for banks and potentially limiting how much business they can conduct with a customer.
The existing rule leaves it to supervisors to impose a 25 percent cap on exposures, meaning each exposure cannot be more than a quarter of the bank's total regulatory capital holdings.
The Basel committee's final rule for all internationally active lenders, sets the same overall cap but makes it mandatory, and based on a more conservative and narrower definition of capital, known as Tier 1. Banks had feared Basel would opt for an even stricter base of core Tier 1 capital.
The committee also responded to feedback from banks and other parties to rein in some of its original plans - a common pattern in the development of new regulations.
It said a bank's exposure to one of the world's top 29 lenders that are deemed to be globally systemically important would be limited to 15 percent, at the top end of the 10-15 percent originally proposed.
It had aired a similar curb on the next tier of lenders, the so-called domestic systemically important banks, and on systemically important non-banks such as clearing houses, but the final rule includes no such requirement.
Banks will have to report any exposure of 10 percent or more, though, higher than the 5 percent initially proposed.
In a big reversal, covered bonds, or debt based on top quality home loans or other assets, will be effectively carved out of rule. The committee's original proposal offered no special treatment to the sector, raising industry hackles.
The committee has also decided to allow some netting of credit default swaps, used by banks to hedge against risks of default in companies or governments.
The scope of the new rule will extended to cover exposures to funds, securitisation structures and collective investment undertakings, the committee said. This brings links between banks and so-called "shadow" or alternative banking more tightly under the regulatory net to allow supervisors to monitor and control risks between the two sectors.
The committee said that by 2016 it would review whether a limit should be set on a bank's exposure to clearing houses, currently exempted, which meet new tougher operating standards.
It will also review if the new rule hinders how central banks conduct monetary policy through money supply.
(Editing by Joshua Franklin and Mark Potter)