To address the classical selectivity estimation problem for OLAP queries in relational databases, a radically different approach calledPlanBouquetwas recently proposed in[1], wherein the estimation process is completely abandoned and replaced with a calibrated discovery mechanism. The beneficial outcome of this new construction is that provable guarantees on worst-case performance, measured as Maximum Sub-Optimality (MSO), are obtained thereby facilitating robust query processing. ThePlanBouquetformulation suffers, however, from a systemic drawback—the MSO bound is a function of not only the query, but also the optimizer's behavioral profile over the underlying database platform. As a result, there are adverse consequences: (i) the bound value becomes highly variable, depending on the specifics of the current operating environment, and (ii) it becomes infeasible to compute the value without substantial investments in preprocessing overheads. In this paper, we first presentSpillBound, a new query processing algorithm that retains the core strength of thePlanBouquetdiscovery process, but reduces the bound dependency to only the query. It does so by incorporating plan termination and selectivity monitoring mechanisms in the database engine. Specifically,SpillBounddelivers a worst-case multiplicative bound, of$D^2+3D$, where$D$is simply the number of error-prone predicates in the user query. Consequently, the bound value becomes independent of the optimizer and the database platform, and the guarantee can be issued simply by query inspection. We go on to prove thatSpillBoundis within an$O(D)$factor of thebest possibledeterministic selectivity discovery algorithm in its class. We next devise techniques to bridge this quadratic-to-linear MSO gap by introducing the notion ofcontour alignment, a characterization of the nature of plan structures along theboundariesof the selectivity space. Specifically, we propose a variant ofSpillBound, calledAlignedBound, which exploits the alignment property and provides a guarantee in the range$\mathbf {[2D+2,D^2+3D]}$. Finally, a detailed empirical evaluation over the standard decision-support benchmarks indicates that: (i)SpillBoundprovides markedly superior performance w.r.t. MSO as compared toPlanBouquet, and (ii)AlignedBoundprovides additional benefits for query instances that are challenging forSpillBound, often coming close to the ideal of MSO linearity in$D$. From an absolute perspective,AlignedBoundevaluates virtually all the benchmark queries considered in our study with MSO of around10or lesser. Therefore, in an overall sense,SpillBoundandAlignedBoundoffer a substantive step forward in the long-standing quest for robust query processing.