Venus Williams and Dinara Safina won through to an intriguing semi-final but the defending champion admitted her sights were already trained on a title showdown with her sister, Serena.

"That would be fantastic, that's what Serena and I are hoping for," said the 29-year-old American and third seed after taking just 68 minutes to eliminate 11th seed Agnieszka Radwanska 6-1, 6-2 in a one-sided quarter final on Court No1.

If a fourth final between the two siblings is to happen, the elder Williams must first overcome world No1 Safina, who beat Sabine Lisicki 6-7, 6-4, 6-1 on Centre Court, and Venus admitted: "We will have to play well and bring our best tennis to the court."

But it looks like she is already achieving that. Against Radwanska, the 20-year-old who reached the quarter-finals last summer, Venus was intimidating and totally ruthless.

She did not concede a point on her serve until her third service game, and even then her hapless opponent required a lucky net cord to beat the five-times champion.

Radwanska could not even hold her own serve until the sixth game of the set, when she finally dragged Williams into a 17-shot rally for game point.

But Williams, showing no ill effects from a heavily strapped left knee, immediately reasserted her authority on her own serve to clinch the set.

Radwanska, the Wimbledon junior champion four years ago, came out fighting in the second set and twice broke Williams' serve. But the Pole was broken three times and the American typically finished it off with an ace.

"That first set was almost perfect and maybe I got a little impatient in the second," she said. "But I'm in the semi-finals of Wimbledon, it's right where I want to be."

Radwanska admitted: "I was trying, but it's very hard to play her if she has a very good day. If she plays like this, she will win one more title."

Elsewhere at the All England Club, Lisicki seemed to relish playing on Centre Court as she took an early break and even afforded herself a smile when Safina benefited from a net cord deflection to enable her to hold serve for 2-3. By contrast, Safina displayed the fragility and inconsistencies that have so far denied her the Grand Slam title her raw talent deserves.

After taking advantage of a sloppy game from the world No41 when she served for the set at 5-4, Safina took the set into the tie-break only to then produce a shocker.

As Lisicki scrambled at the baseline, Safina was forced into going for more on her shots and errors ensued. Lisicki blew two set points - the second of which thanks to an appalling forehand struck wide with the court at her mercy but Safina then served a seventh double fault of the set to gift her opponent the opener in 58 minutes.

The second set went with serve until the seventh game, when Lisicki tightened up and double faulted on break point. Safina, who looked a tormented figure throughout, then survived a break point on her own serve before eventually levelling the match.

The pair then exchanged three breaks at the start of the final set before Safina wrestled control of the match with a double break to close it out thanks to a Lisicki error.

In the other half of the draw, Elena Dementieva, the fourth seed from Russia, booked her place in the semi-finals with a 6-2, 6-2 victory against Italy's Francesca Schiavone.