(Adds quotes and background, European Commission comment)

By Michael Shields

ZURICH, Dec 1 (Reuters) - Swiss efforts to curb immigration from the European Union without provoking a clash with Brussels cleared another hurdle on Thursday when parliament's upper house backed giving locals first crack at open jobs rather than adopting outright quotas.

The step is roughly in line with a bill the lower house adopted in September, skirting direct confrontation with the EU which has insisted on free movement of people, a key condition for enhanced Swiss access to the single market.

The two bills still must be reconciled ahead of a final vote later this month, but both stop short of upper limits and quotas on immigration that Swiss voters demanded in a binding 2014 referendum.

How the EU reacts to the legislation will be scrutinised for hints of what Britain might expect as it negotiates terms of its EU exit after voting in June to quit the bloc.

"What is important for the European Commission is that there is no discrimination between Swiss citizens and EU citizens," a European Commission spokeswoman told a news conference in Brussels. She declined further comment until the final Swiss legislation was in place.

Should Brussels determine the final measure infringes too heavily on freedom of movement, it could cancel other bilateral accords which ease Swiss trade with the EU in areas that account for 7 percent of Swiss economic output.

But diplomats do not expect Brussels to take such a drastic line unless Switzerland formally cancels the free movement accord that came into force in 2002. It has covered the EU-15 states plus Malta and Cyprus since June 2007, and expanded since then to other EU and EFTA countries.

The far-right Swiss People's Party (SVP), the biggest faction in parliament, had argued in vain to translate the 2014 referendum into quotas by the deadline of February 2017.

Upper house member Peter Foehn, an SVP politician, told the debate that net immigration had risen by more than 750,000 since 2007. "When I look at tiny Switzerland that is much too much," he said.

Around 8.3 million people live in the neutral Alpine republic, nearly a quarter of them foreign.

Proponents of the compromise immigration package have called it a compromise meant to curb the foreign influx without violating free movement rules. They hope the EU will find it tolerable despite the Brexit vote complication.

"The bilaterals should not be put at risk," said Philipp Mueller, an architect of the Swiss measure and parliament member from the pro-business Free Democrats.

In any event, Swiss voters may well be asked again to choose between close ties with its main trading partner and immigration curbs, the government said in October.

(Additonal reporting by Gabriela Baczynska in Brussels; Editing by Toby Chopra) ((Michael.Shields@thomsonreuters.com; +41 58 306 7461; Reuters Messaging: michael.shields.thomsonreuters.com@reuters.net))