Given a pseudo-effective divisor L we construct the diminished ideal 𝒥 σ ( L ) , a “continuous” extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. Our main theorem shows that for most pseudo-effective divisors L the multiplier ideal 𝒥 ( h min ) of the metric of minimal singularities on 𝒪 X ( L ) is contained in 𝒥 σ ( L ) . We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.