Sept 28 (Reuters) - Belarus was choosing a new parliament on Sunday in an election veteran President Alexander Lukashenko hopes will win Western endorsement he can translate into better relations with Washington and the European Union.

Lukashenko, in power for 14 years, is accused by the West of rigging elections, muzzling the media and hounding the opposition.

Following are key points on the significance of the vote:

* The West has said its relations with Belarus could improve if the elections are deemed free and fair, after courts ordered the release of the last Belarussian detainees the West considered political prisoners.

* Lukashenko wants to improve ties with the West after a row with traditional ally Russia over gas prices last year. He has said he wants the opposition to win some seats in parliament. The opposition has said it could win 20-30 seats out of 110.

* The European Union and the United States could drop a travel ban on Lukashenko and government officials and ease financial sanctions, which would draw Belarus closer to the West and provide impetus for foreign investment.

* No election in Belarus has been deemed free or fair since the mid-1990s. The opposition failed to elect a single member to parliament in 2004.

* Election officials have registered 265 candidates, including about 70 from opposition parties -- far more than in previous elections.

* The often fractious opposition rejected calls by some activists for a boycott of the election, despite complaints that it would be granted no access to commissions overseeing the count at polling stations.