When marketers increase their Facebook ad buying, their paid search conversion rates jump—up to a point, according to a new report by Kenshoo Ltd.

Consumers exposed to a brand’s Facebook ads had an 11% higher conversion rate than those who didn’t see the ads, according to the report “Sweet Spot,” which is based on an analysis of Experian clients’ performance data from Jan. 30 to Feb. 14.

The study was commissioned by Facebook Inc., but advertisers did not receive free impressions from the social network in exchange for participation. The study organized consumers into four groups—those only exposed to paid search advertising and those exposed to low, medium and high spending levels of Facebook advertising.

Exposing consumers to Facebook ads paid off for the marketers in the study after weighing the value of additional conversions compared to the Facebook ads’ costs, the report suggests. Moreover, the boost to marketers’ conversion rates helped fuel a 10% drop in advertisers’ cost per acquisition across the three groups exposed to Facebook ads.

The results make sense, the report suggests, because consumers perceive their relationships with brands to be a single conversation regardless of where, when and how they engage with the company. “They generally don’t make a conscious decision between channels, devices and promotions, but rather consume a unique mix of a brand’s media and advertising which sometimes can influence consumers to become customers—and sometimes not,” the report says.

However, there’s a limit to how much additional Facebook ad spending appears to influence paid search conversions, the report says. In fact, the group exposed to the middle level of Facebook ad spending had the highest conversion rate and lowest cost per acquisition, which suggests that there’s a “sweet spot” that advertisers can hit to get the most effect per dollar spent.

“The data is clear that this synergy does exist and it’s now up to you to figure out how this cross-channel force can be harnessed in your marketing environment,” the report says.