diff --git a/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LineSearch.java b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LineSearch.java
index 310af671a..7763e7788 100644
--- a/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LineSearch.java
+++ b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/LineSearch.java
@@ -54,6 +54,11 @@ public class LineSearch {
      * Automatic bracketing.
      */
     private final BracketFinder bracket = new BracketFinder();
+    /**
+     * Extent of the initial interval used to find an interval that
+     * brackets the optimum.
+     */
+    private final double initialBracketingRange;
     /**
      * Optimizer on behalf of which the line search must be performed.
      */
@@ -70,23 +75,33 @@ public class LineSearch {
      * @param optimizer Optimizer on behalf of which the line search
      * be performed.
      * Its {@link MultivariateOptimizer#computeObjectiveValue(double[])
-     * computeObjectiveValue} method will be called by this class's
+     * computeObjectiveValue} method will be called by the
      * {@link #search(double[],double[]) search} method.
-     * @param relativeTolerance Relative threshold.
-     * @param absoluteTolerance Absolute threshold.
+     * @param relativeTolerance Search will stop when the function relative
+     * difference between successive iterations is smaller than this value.
+     * @param absoluteTolerance Search will stop when the function absolute
+     * difference between successive iterations is smaller than this value.
+     * @param initialBracketingRange Extent of the initial interval used to
+     * find an interval that brackets the optimum.
+     * If the optimized function varies a lot in the vicinity of the optimum,
+     * it may be necessary to provide a value lower than the distance between
+     * successive local minima.
      */
     public LineSearch(MultivariateOptimizer optimizer,
                       double relativeTolerance,
-                      double absoluteTolerance) {
+                      double absoluteTolerance,
+                      double initialBracketingRange) {
         mainOptimizer = optimizer;
         lineOptimizer = new BrentOptimizer(REL_TOL_UNUSED,
                                            ABS_TOL_UNUSED,
                                            new SimpleUnivariateValueChecker(relativeTolerance,
                                                                             absoluteTolerance));
+        this.initialBracketingRange = initialBracketingRange;
     }
 
     /**
-     * Find the minimum of the function {@code f(p + alpha * d)}.
+     * Finds the number {@code alpha} that optimizes
+     * {@code f(startPoint + alpha * direction)}.
      *
      * @param startPoint Starting point.
      * @param direction Search direction.
@@ -109,7 +124,7 @@ public class LineSearch {
             };
 
         final GoalType goal = mainOptimizer.getGoalType();
-        bracket.search(f, goal, 0, 1);
+        bracket.search(f, goal, 0, initialBracketingRange);
         // Passing "MAX_VALUE" as a dummy value because it is the enclosing
         // class that counts the number of evaluations (and will eventually
         // generate the exception).
diff --git a/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/gradient/NonLinearConjugateGradientOptimizer.java b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/gradient/NonLinearConjugateGradientOptimizer.java
index 3790436f1..5cdb838b3 100644
--- a/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/gradient/NonLinearConjugateGradientOptimizer.java
+++ b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/gradient/NonLinearConjugateGradientOptimizer.java
@@ -86,7 +86,9 @@ public class NonLinearConjugateGradientOptimizer
      * search.
      *
      * @since 3.1
-     * @deprecated As of v3.3, class is not used anymore.
+     * @deprecated As of v3.3, this class is not used anymore.
+     * This setting is replaced by the {@code initialBracketingRange}
+     * argument to the new constructors.
      */
     @Deprecated
     public static class BracketingStep implements OptimizationData {
@@ -125,6 +127,7 @@ public class NonLinearConjugateGradientOptimizer
              checker,
              1e-8,
              1e-8,
+             1e-8,
              new IdentityPreconditioner());
     }
 
@@ -137,7 +140,7 @@ public class NonLinearConjugateGradientOptimizer
      * @param checker Convergence checker.
      * @param lineSearchSolver Solver to use during line search.
      * @deprecated as of 3.3. Please use
-     * {@link #NonLinearConjugateGradientOptimizer(Formula,ConvergenceChecker,double,double)} instead.
+     * {@link #NonLinearConjugateGradientOptimizer(Formula,ConvergenceChecker,double,double,double)} instead.
      */
     @Deprecated
     public NonLinearConjugateGradientOptimizer(final Formula updateFormula,
@@ -158,17 +161,23 @@ public class NonLinearConjugateGradientOptimizer
      * @param checker Convergence checker.
      * @param relativeTolerance Relative threshold for line search.
      * @param absoluteTolerance Absolute threshold for line search.
+     * @param initialBracketingRange Extent of the initial interval used to
+     * find an interval that brackets the optimum in order to perform the
+     * line search.
      *
-     * @see LineSearch#LineSearch(MultivariateOptimizer,double,double)
+     * @see LineSearch#LineSearch(MultivariateOptimizer,double,double,double)
+     * @since 3.3
      */
     public NonLinearConjugateGradientOptimizer(final Formula updateFormula,
                                                ConvergenceChecker<PointValuePair> checker,
                                                double relativeTolerance,
-                                               double absoluteTolerance) {
+                                               double absoluteTolerance,
+                                               double initialBracketingRange) {
         this(updateFormula,
              checker,
              relativeTolerance,
              absoluteTolerance,
+             initialBracketingRange,
              new IdentityPreconditioner());
     }
 
@@ -180,7 +189,7 @@ public class NonLinearConjugateGradientOptimizer
      * @param lineSearchSolver Solver to use during line search.
      * @param preconditioner Preconditioner.
      * @deprecated as of 3.3. Please use
-     * {@link #NonLinearConjugateGradientOptimizer(Formula,ConvergenceChecker,double,double,Preconditioner)} instead.
+     * {@link #NonLinearConjugateGradientOptimizer(Formula,ConvergenceChecker,double,double,double,Preconditioner)} instead.
      */
     @Deprecated
     public NonLinearConjugateGradientOptimizer(final Formula updateFormula,
@@ -191,6 +200,7 @@ public class NonLinearConjugateGradientOptimizer
              checker,
              lineSearchSolver.getRelativeAccuracy(),
              lineSearchSolver.getAbsoluteAccuracy(),
+             lineSearchSolver.getAbsoluteAccuracy(),
              preconditioner);
     }
 
@@ -202,13 +212,18 @@ public class NonLinearConjugateGradientOptimizer
      * @param preconditioner Preconditioner.
      * @param relativeTolerance Relative threshold for line search.
      * @param absoluteTolerance Absolute threshold for line search.
+     * @param initialBracketingRange Extent of the initial interval used to
+     * find an interval that brackets the optimum in order to perform the
+     * line search.
      *
-     * @see LineSearch#LineSearch(MultivariateOptimizer,double,double)
+     * @see LineSearch#LineSearch(MultivariateOptimizer,double,double,double)
+     * @since 3.3
      */
     public NonLinearConjugateGradientOptimizer(final Formula updateFormula,
                                                ConvergenceChecker<PointValuePair> checker,
                                                double relativeTolerance,
                                                double absoluteTolerance,
+                                               double initialBracketingRange,
                                                final Preconditioner preconditioner) {
         super(checker);
 
@@ -216,7 +231,8 @@ public class NonLinearConjugateGradientOptimizer
         this.preconditioner = preconditioner;
         line = new LineSearch(this,
                               relativeTolerance,
-                              absoluteTolerance);
+                              absoluteTolerance,
+                              initialBracketingRange);
     }
 
     /**
diff --git a/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/PowellOptimizer.java b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/PowellOptimizer.java
index 475fe4ef7..16d5253ff 100644
--- a/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/PowellOptimizer.java
+++ b/src/main/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/PowellOptimizer.java
@@ -127,7 +127,8 @@ public class PowellOptimizer
         // Create the line search optimizer.
         line = new LineSearch(this,
                               lineRel,
-                              lineAbs);
+                              lineAbs,
+                              1d);
     }
 
     /**
diff --git a/src/main/java/org/apache/commons/math3/optim/univariate/BracketFinder.java b/src/main/java/org/apache/commons/math3/optim/univariate/BracketFinder.java
index ef2af5267..f83031ba5 100644
--- a/src/main/java/org/apache/commons/math3/optim/univariate/BracketFinder.java
+++ b/src/main/java/org/apache/commons/math3/optim/univariate/BracketFinder.java
@@ -110,7 +110,10 @@ public class BracketFinder {
      * @throws TooManyEvaluationsException if the maximum number of evaluations
      * is exceeded.
      */
-    public void search(UnivariateFunction func, GoalType goal, double xA, double xB) {
+    public void search(UnivariateFunction func,
+                       GoalType goal,
+                       double xA,
+                       double xB) {
         evaluations.resetCount();
         final boolean isMinim = goal == GoalType.MINIMIZE;
 
diff --git a/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/gradient/NonLinearConjugateGradientOptimizerTest.java b/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/gradient/NonLinearConjugateGradientOptimizerTest.java
index 6307c89c3..66733683d 100644
--- a/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/gradient/NonLinearConjugateGradientOptimizerTest.java
+++ b/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/gradient/NonLinearConjugateGradientOptimizerTest.java
@@ -105,7 +105,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         optimizer.optimize(new MaxEval(100),
                            problem.getObjectiveFunction(),
                            problem.getObjectiveFunctionGradient(),
@@ -122,7 +122,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -145,7 +145,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -171,7 +171,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -193,7 +193,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -235,7 +235,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
            = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                      new SimpleValueChecker(1e-13, 1e-13),
-                                                     1e-7, 1e-7,
+                                                     1e-7, 1e-7, 1,
                                                      preconditioner);
 
         PointValuePair optimum
@@ -267,7 +267,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -288,7 +288,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-13, 1e-13),
-                                                      1e-15, 1e-15);
+                                                      1e-15, 1e-15, 1);
         PointValuePair optimum1
             = optimizer.optimize(new MaxEval(200),
                                  problem1.getObjectiveFunction(),
@@ -333,7 +333,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -356,7 +356,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
            = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                      new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                     1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -377,7 +377,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -400,7 +400,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
             = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                       new SimpleValueChecker(1e-6, 1e-6),
-                                                      1e-3, 1e-3);
+                                                      1e-3, 1e-3, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),
@@ -422,7 +422,7 @@ public class NonLinearConjugateGradientOptimizerTest {
         NonLinearConjugateGradientOptimizer optimizer
            = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                      new SimpleValueChecker(1e-30, 1e-30),
-                                                     1e-15, 1e-13);
+                                                     1e-15, 1e-13, 1);
         PointValuePair optimum
             = optimizer.optimize(new MaxEval(100),
                                  problem.getObjectiveFunction(),