As the propensity of premium store brands (SBs) increases, retailers must consider different ways to drive sales besides promotional strategies. With this in mind, we consider a national brand (NB) and a (premium) SB co-existing in a market. Each brand has to decide the amount to invest in advertising its product and the prices to charge its customers, which can be determined separately or in unison. When either advertising expenditures or pricing decisions are set, each brand must keep in mind that the advertising efforts and revenue may spillover between the two brands, customers who intend to purchase the NB may end up purchasing the SB and vice versa. We derive an analytical model of the situations described and characterize equilibrium advertising decisions. We find that the characteristics of a premium SB may depend on which marketing/promoting instrument (advertising or pricing) is the primary method for driving demand; and in some situations an NB may be better off to not advertise at all and instead let the premium SB carry out all of the advertising.