diff --git a/opm/autodiff/BlackoilModelBase_impl.hpp b/opm/autodiff/BlackoilModelBase_impl.hpp
index 249b4f550..f53fe75cf 100644
--- a/opm/autodiff/BlackoilModelBase_impl.hpp
+++ b/opm/autodiff/BlackoilModelBase_impl.hpp
@@ -248,7 +248,8 @@ namespace detail {
         asImpl().assemble(reservoir_state, well_state, iteration == 0);
         residual_norms_history_.push_back(asImpl().computeResidualNorms());
         const bool converged = asImpl().getConvergence(dt, iteration);
-        if (!converged) {
+        const bool must_solve = (iteration < nonlinear_solver.minIter()) || (!converged);
+        if (must_solve) {
             // Compute the nonlinear update.
             V dx = asImpl().solveJacobianSystem();
 
@@ -271,7 +272,7 @@ namespace detail {
             asImpl().updateState(dx, reservoir_state, well_state);
         }
         const bool failed = false; // Not needed in this model.
-        const int linear_iters = converged ? 0 : asImpl().linearIterationsLastSolve();
+        const int linear_iters = must_solve ? asImpl().linearIterationsLastSolve() : 0;
         return IterationReport{ failed, converged, linear_iters };
     }
 
diff --git a/opm/autodiff/NonlinearSolver.hpp b/opm/autodiff/NonlinearSolver.hpp
index 134de8fc9..f6632a448 100644
--- a/opm/autodiff/NonlinearSolver.hpp
+++ b/opm/autodiff/NonlinearSolver.hpp
@@ -113,6 +113,18 @@ namespace Opm {
         /// The step-change size for the relaxation factor.
         double relaxIncrement() const    { return param_.relax_increment_; }
 
+        /// The relaxation type (DAMPEN or SOR).
+        enum RelaxType relaxType() const { return param_.relax_type_; }
+
+        /// The relaxation relative tolerance.
+        double relaxRelTol() const       { return param_.relax_rel_tol_; }
+
+        /// The maximum number of nonlinear iterations allowed.
+        double maxIter() const           { return param_.max_iter_; }
+
+        /// The minimum number of nonlinear iterations allowed.
+        double minIter() const           { return param_.min_iter_; }
+
     private:
         // ---------  Data members  ---------
         SolverParameters param_;
@@ -121,12 +133,6 @@ namespace Opm {
         unsigned int linearIterations_;
         unsigned int nonlinearIterationsLast_;
         unsigned int linearIterationsLast_;
-
-        // ---------  Private methods  ---------
-        enum RelaxType relaxType() const { return param_.relax_type_; }
-        double relaxRelTol() const       { return param_.relax_rel_tol_; }
-        double maxIter() const           { return param_.max_iter_; }
-        double minIter() const           { return param_.min_iter_; }
     };
 } // namespace Opm
 
diff --git a/opm/autodiff/NonlinearSolver_impl.hpp b/opm/autodiff/NonlinearSolver_impl.hpp
index 984b54d42..6e7dce2c9 100644
--- a/opm/autodiff/NonlinearSolver_impl.hpp
+++ b/opm/autodiff/NonlinearSolver_impl.hpp
@@ -93,21 +93,21 @@ namespace Opm
 
         // ----------  Main nonlinear solver loop  ----------
         do {
+            // Do the nonlinear step. If we are in a converged state, the
+            // model will usually do an early return without an expensive
+            // solve, unless the minIter() count has not been reached yet.
             IterationReport report = model_->nonlinearIteration(iteration, dt, *this, reservoir_state, well_state);
             if (report.failed) {
                 OPM_THROW(Opm::NumericalProblem, "Failed to complete a nonlinear iteration.");
             }
-            if (report.converged) {
-                assert(report.linear_iterations == 0);
-                converged = true;
-            }
+            converged = report.converged;
             linIters += report.linear_iterations;
             ++iteration;
-        } while ( (!converged && (iteration <= maxIter())) || (minIter() > iteration));
+        } while ( (!converged && (iteration <= maxIter())) || (iteration <= minIter()));
 
         if (!converged) {
             if (model_->terminalOutputEnabled()) {
-                std::cerr << "WARNING: Failed to compute converged solution in " << iteration << " iterations." << std::endl;
+                std::cerr << "WARNING: Failed to compute converged solution in " << iteration - 1 << " iterations." << std::endl;
             }
             return -1; // -1 indicates that the solver has to be restarted
         }