Do environments or species traits that lower the mortality of individuals create selection for delaying senescence? Reading the literature creates an impression that mathematically oriented biologists cannot agree on the validity of George Williams' prediction (who claimed 'yes'). The abundance of models and opinions may bewilder those that are new to the field. Here we provide heuristics as well as simple models that outline when the Williams prediction holds, why there is a 'null model' where extrinsic mortality does not matter, and why it is also possible to expect the opposite of Williams' prediction: increased extrinsic mortality favours slower senescence. While most existing theory focuses on interpreting differences in selection gradients, we hope to offer intuition by quantifying how much delaying the 'placement' of an offspring into the population reduces its expected contribution to the gene pool of the future. Our first example shows why the null result arises and why the null can stop being valid in models that consider population regulation. Thereafter, a model with 10 different choices for density dependence shows why extrinsic mortality has the power to favour slow life histories on the fast-slow continuum, but this requires that density-dependent effects harm juveniles.