The effectiveness of Data Injections Attacks (DIAs) critically depends on the completeness of the system information accessible to adversaries. This relationship positions information incompleteness enhancement as a vital defense strategy for degrading DIA performance. In this paper, we focus on the information-theoretic stealth attacks, where the attacker encounters a fundamental tradeoff between the attack stealthiness and destructiveness. Specifically, we systematically characterize how incomplete admittance information impacts the dual objectives. In particular, we establish sufficient conditions for two distinct operational regimes: (i) stealthiness intensifies while destructive potential diminishes and (ii) destructiveness increases while stealth capability weakens. For scenarios beyond these regimes, we propose a maximal incompleteness strategy to optimally degrade stealth capability. To solve the associated optimization problem, the feasible region is reduced without excluding the optimal solution, and a heuristic algorithm is then introduced to effectively identify the near-optimal solutions within the reduced region. Numerical simulations are conducted on IEEE test systems to validate the findings.