Nissan’s position trailing Honda is a particular vexation for Carlos Ghosn, Nissan’s famously demanding boss.  According to Nissan executives in the U.S., Ghosn is prodding his legions to erase the gap, pointing out that while the automaker outpaces Honda globally, in terms of unit sales – it’s behind in the U.S.

Ghosn has demanded to know from subordinates why Nissan sells a bigger variety of models in the U.S. yet fewer total vehicles?  The point, according to Nissan executives, is that Honda gets its sales by concentrating on “core” models, led by Civic and Accord. Addressing this disparity, Nissan recently dropped its Murano convertible and Altima coupe, for which demand is limited.

“Our product portfolio is broader than theirs,” acknowledged Pierre Loing, head of Nissan’s vehicle development in the U.S. “But ours is going to get narrower and stronger.”  Within hours of his comment, Nissan disclosed that its idiosyncratic Cube small crossover was being dropped from the U.S. lineup for 2015.

Honda, with a long and stellar reputation in the U.S., has built its sales on Civic and Accord sedans, as well as CR-V compact crossover and Odyssey minivan, usually rated tops in its category. Honda is regarded as the blander and more reliable of second-tier rivals.

Nissan, which benefits from edgier and more expressive styling, sells 18 models in the U.S., not counting the soon-to-be-departed Cube.

In 2013, Nissan and its associated brands, such as Infiniti, grabbed a 6.2% share of the world automotive market, to Honda’s 5.2%.  (Toyota was first with 12%)  In the U.S. last year, Honda had 9.8% share to Nissan’s 8%, a lead of about 280,000 vehicles sold.

This year, through June, Nissan had narrowed the share lead to 0.5 points, with Nissan at 8.6 and Honda at 9.1.  Which implies a lead of about 40,000 vehicles.

Some of the narrowing may be attributed to pressure from Paris, where Ghosn presides over Nissan and its alliance partner Renault SA.  He hasn’t been shy about sacking executives who disappoint and replacing them with new blood.

Jose Munoz, who led Nissan’s operations in Mexico to the lead there now runs the U.S., assisted by Fred Diaz, who left Chrysler to become head of U.S. sales and marketing. Both are regarded as hard-chargers.

“Among the issues Nissan may have in capturing market share from Honda in the US over the coming years is the competitiveness of the US market—this is far from a two-player market, of course,” said Stephanie Brinley, senior analyst for IHS Automotive.  “To increase market share, Nissan has to conquest across all mainstream brands; it could increase share over time without necessarily taking it from Honda.”

Nissan’s core models – Altima, Sentra, Rogue, Pathfinder, Versa – could be joined by a sixth, if the new Titan pickup scheduled to debut next year can make a dent among its stronger competition.  If not, the Nissan brain trust may have to decide if it’s significant enough to renew one more time.

In the meantime, expect a down-and-dirty battle of clever discounting and marketing gambits as Nissan battles Honda for every new-vehicle sale.