The Pareto secretary problem asks to select online a Pareto‑maximal observation from an i.i.d. stream, meaning no other observation is at least as good in every coordinate and strictly better in one.\ \ For any fixed dimension $d\ge2$ with independent continuous coordinates, the optimal failure probability scales as $\frac{1}{(\log n)^{d-1}\log\log n}$. This order holds both with full information and when only coordinate ranks are available. A deterministic rank rule attains the optimal leading term uniformly over all marginal distributions.\ \ When the coordinates follow any positive‑definite Gaussian covariance, the same failure order persists, with a leading constant that depends on the correlation matrix. Moreover, a rank‑based rule reaches the optimal leading failure probability without knowing the Gaussian parameters.\ \ In both models we identify the optimal fixed cutoff and its leading constant; its failure probability exceeds the unrestricted optimum by a factor $\Theta_d((\log\log n)^2)$.\ \ Under arbitrary dependence, a fixed joint density with uniform marginals can yield a full‑information success rate approaching about $0.58$.\ \ The proof exploits the scarcity of observations whose domination probability is extremely small to bound any stopping rule. A matching rule selects the currently maximal point when this probability falls below a threshold that rises as time runs out. Coordinate ranks obtained from an initial sample provide sufficiently accurate estimates to preserve the optimal leading failure probability.\ \ For singular Gaussian distributions with known correlations, we characterize the optimal failure asymptotics achievable using ranks. Singular dependence can make every observation acceptable or recover the difficulty of selecting a single best point.\ \ Review