Simple estimators of the parameters σ, β and σ of the simple linear regression model, based upon trimmed samples, and called adjusted Trimmed Estimators (ATE) are introduced. They are very easy to compute, and their coefficients may be chosen so that their efficiency relative to the (O-BLUE) from complete samples is equal to one. The coefficients are given for five symmetric distributions, namely, the normal distribution, the scale contaminated normal distributions with a scale factor of σ = 3.0 and contamination proportions ∊ = 0.01, .05 and .1O and the double exponential distribution, for values of 5 ≤n≤ 20 and different amounts of trimming (g). The estimators are shown to be biased, but the exact amounts of bias are given. Adjusted Efficiency Robust Estimators (AERE) are also introduced. They are shown to maintain high efficiency relative to the (O-BLUE) under changes in the distribution of the errors.