diff --git a/src/Learning/DTForest/DTDiscretizerMODL.cpp b/src/Learning/DTForest/DTDiscretizerMODL.cpp
index 53ef284c5..c4093ebdf 100644
--- a/src/Learning/DTForest/DTDiscretizerMODL.cpp
+++ b/src/Learning/DTForest/DTDiscretizerMODL.cpp
@@ -290,7 +290,7 @@ void DTDiscretizerMODL::DiscretizeNEW(KWFrequencyTable* kwftSource, KWFrequencyT
 			// delete kwftMergedTable;
 			// kwftMergedTable = NULL;
 
-			if (dCost < dBestCost)
+			if (dCost < dBestCost - dEpsilon)
 			{
 				dBestCost = dCost;
 				// Destruction de l'optimum precedent
@@ -469,7 +469,7 @@ void DTDiscretizerMODL::DiscretizeOLD(KWFrequencyTable* kwftSource, KWFrequencyT
 				delete kwftMergedTable;
 				kwftMergedTable = NULL;
 
-				if (dCost < dBestCost)
+				if (dCost < dBestCost - dEpsilon)
 				{
 					dBestCost = dCost;
 					// Destruction de l'optimum precedent
@@ -630,7 +630,7 @@ void DTDiscretizerMODL::DiscretizeGranularizedFrequencyTableNEW(KWFrequencyTable
 				kwdfvSourceFrequencyVectortarget1->CopyFrom(kwdfvSourceFrequencyVector1);
 				nvfmax = nfv;
 			}
-			if (dCost < dBestCost)
+			if (dCost < dBestCost - dEpsilon)
 			{
 				// cout << "cout best " << nfv + 1 << " : " << dCost << endl;
 				dBestCost = dCost;
@@ -643,7 +643,7 @@ void DTDiscretizerMODL::DiscretizeGranularizedFrequencyTableNEW(KWFrequencyTable
 
 		// cout << "nvfmax / nsourcesize : " << nvfmax << " / " << nsourcesize << endl;
 
-		if (dCostnull < dBestCost)
+		if (dCostnull < dBestCost + dEpsilon)
 		{
 			// cout << "NULL Cost" << endl;
 			// cout << "cout best " << nfv + 1 << " : " << dCost << endl;
diff --git a/src/Learning/DTForest/DTGrouperMODL.cpp b/src/Learning/DTForest/DTGrouperMODL.cpp
index 654c2b974..d0ae9453e 100644
--- a/src/Learning/DTForest/DTGrouperMODL.cpp
+++ b/src/Learning/DTForest/DTGrouperMODL.cpp
@@ -501,7 +501,7 @@ void DTGrouperMODL::GroupPreprocessedTable(KWFrequencyTable* kwftSource, KWFrequ
 			dCost = ComputeGroupingCost(kwftOptimizedGranularizedTable, nCurrentPartileNumber);
 
 			// Cas de l'amelioration du cout
-			if (dCost < dBestCost)
+			if (dCost < dBestCost - dEpsilon)
 			{
 				// Memorisation du cout optimal
 				dBestCost = dCost;
@@ -715,7 +715,7 @@ void DTGrouperMODL::SmallSourceNumberGroup(KWFrequencyTable* kwftSource, KWFrequ
 		MergeFrequencyVectors(workingFrequencyVector, kwftSource->GetFrequencyVectorAt(1),
 				      kwftSource->GetFrequencyVectorAt(2));
 		dCost = ComputeGroupCost(workingFrequencyVector) + dCostGroup0;
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 			nBestTwoGroupsIndex = 0;
@@ -724,7 +724,7 @@ void DTGrouperMODL::SmallSourceNumberGroup(KWFrequencyTable* kwftSource, KWFrequ
 		MergeFrequencyVectors(workingFrequencyVector, kwftSource->GetFrequencyVectorAt(0),
 				      kwftSource->GetFrequencyVectorAt(2));
 		dCost = ComputeGroupCost(workingFrequencyVector) + dCostGroup1;
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 			nBestTwoGroupsIndex = 1;
@@ -733,7 +733,7 @@ void DTGrouperMODL::SmallSourceNumberGroup(KWFrequencyTable* kwftSource, KWFrequ
 		MergeFrequencyVectors(workingFrequencyVector, kwftSource->GetFrequencyVectorAt(0),
 				      kwftSource->GetFrequencyVectorAt(1));
 		dCost = ComputeGroupCost(workingFrequencyVector) + dCostGroup2;
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 			nBestTwoGroupsIndex = 2;
diff --git a/src/Learning/KWDataPreparation/KWDiscretizerMODL.cpp b/src/Learning/KWDataPreparation/KWDiscretizerMODL.cpp
index b0361c3c2..d7004c161 100644
--- a/src/Learning/KWDataPreparation/KWDiscretizerMODL.cpp
+++ b/src/Learning/KWDataPreparation/KWDiscretizerMODL.cpp
@@ -194,7 +194,7 @@ void KWDiscretizerMODL::Discretize(KWFrequencyTable* kwftSource, KWFrequencyTabl
 				delete kwftMergedTable;
 				kwftMergedTable = NULL;
 
-				if (dCost < dBestCost)
+				if (dCost < dBestCost - dEpsilon)
 				{
 					dBestCost = dCost;
 					// Destruction de l'optimum precedent
diff --git a/src/Learning/KWDataPreparation/KWGrouperMODL.cpp b/src/Learning/KWDataPreparation/KWGrouperMODL.cpp
index 7a11413f6..da4b1c98f 100644
--- a/src/Learning/KWDataPreparation/KWGrouperMODL.cpp
+++ b/src/Learning/KWDataPreparation/KWGrouperMODL.cpp
@@ -594,7 +594,7 @@ void KWGrouperMODL::GroupPreprocessedTable(KWFrequencyTable* kwftSource, KWFrequ
 			dCost = ComputeGroupingCost(kwftOptimizedGranularizedTable, nCurrentPartileNumber);
 
 			// Cas de l'amelioration du cout
-			if (dCost < dBestCost)
+			if (dCost < dBestCost - dEpsilon)
 			{
 				// Memorisation du cout optimal
 				dBestCost = dCost;
@@ -813,7 +813,7 @@ void KWGrouperMODL::SmallSourceNumberGroup(KWFrequencyTable* kwftSource, KWFrequ
 		MergeFrequencyVectors(workingFrequencyVector, kwftSource->GetFrequencyVectorAt(1),
 				      kwftSource->GetFrequencyVectorAt(2));
 		dCost = ComputeGroupCost(workingFrequencyVector) + dCostGroup0;
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 			nBestTwoGroupsIndex = 0;
@@ -822,7 +822,7 @@ void KWGrouperMODL::SmallSourceNumberGroup(KWFrequencyTable* kwftSource, KWFrequ
 		MergeFrequencyVectors(workingFrequencyVector, kwftSource->GetFrequencyVectorAt(0),
 				      kwftSource->GetFrequencyVectorAt(2));
 		dCost = ComputeGroupCost(workingFrequencyVector) + dCostGroup1;
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 			nBestTwoGroupsIndex = 1;
@@ -831,7 +831,7 @@ void KWGrouperMODL::SmallSourceNumberGroup(KWFrequencyTable* kwftSource, KWFrequ
 		MergeFrequencyVectors(workingFrequencyVector, kwftSource->GetFrequencyVectorAt(0),
 				      kwftSource->GetFrequencyVectorAt(1));
 		dCost = ComputeGroupCost(workingFrequencyVector) + dCostGroup2;
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 			nBestTwoGroupsIndex = 2;
diff --git a/src/Learning/KWTest/KWDensityEstimationTest.cpp b/src/Learning/KWTest/KWDensityEstimationTest.cpp
index e125da8aa..32900b729 100644
--- a/src/Learning/KWTest/KWDensityEstimationTest.cpp
+++ b/src/Learning/KWTest/KWDensityEstimationTest.cpp
@@ -183,7 +183,7 @@ int KWDensityEstimationTest::SearchBestInstanceGridSize(ContinuousVector* cvXVal
 			cout << nAxisCellNumber << "\t" << dCost << endl;
 
 		// Test si amelioration
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 			nBestAxisCellNumber = nAxisCellNumber;
diff --git a/src/Learning/MHHistograms/MHDiscretizerHistogramMODL.cpp b/src/Learning/MHHistograms/MHDiscretizerHistogramMODL.cpp
index 51403cbf2..d2ce5fce7 100644
--- a/src/Learning/MHHistograms/MHDiscretizerHistogramMODL.cpp
+++ b/src/Learning/MHHistograms/MHDiscretizerHistogramMODL.cpp
@@ -647,7 +647,7 @@ void MHDiscretizerHistogramMODL::GranularizedDiscretizeValues(const ContinuousVe
 			     << KWContinuous::ContinuousToString(dCost) << endl;
 
 		// Memorisation si amelioration du cout
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 			if (optimizedHistogramFrequencyTable != NULL)
diff --git a/src/Learning/MHHistograms/MHDiscretizerHistogramMODL_fp.cpp b/src/Learning/MHHistograms/MHDiscretizerHistogramMODL_fp.cpp
index 6a36ebac6..eeac16ae9 100644
--- a/src/Learning/MHHistograms/MHDiscretizerHistogramMODL_fp.cpp
+++ b/src/Learning/MHHistograms/MHDiscretizerHistogramMODL_fp.cpp
@@ -743,7 +743,7 @@ void MHDiscretizerHistogramMODL_fp::OptimizeGranularity(MHHistogram*& optimizedH
 		delete optimizedHistogramFrequencyTable;
 
 		// Memorisation si amelioration du cout
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;
 
diff --git a/src/Learning/MHHistograms/MHFloatingPointFrequencyTableBuilder.cpp b/src/Learning/MHHistograms/MHFloatingPointFrequencyTableBuilder.cpp
index 02b9ad97e..607ec1554 100644
--- a/src/Learning/MHHistograms/MHFloatingPointFrequencyTableBuilder.cpp
+++ b/src/Learning/MHHistograms/MHFloatingPointFrequencyTableBuilder.cpp
@@ -2127,6 +2127,7 @@ int MHFloatingPointFrequencyTableBuilder::SearchBinIndex(int nSearchedCumulative
 void MHFloatingPointFrequencyTableBuilder::InitializeDomainBounds()
 {
 	boolean bDisplay = false;
+	const double dEpsilon = 1e-7;
 	int nTotalFrequency;
 	int i;
 	double dBestCost;
@@ -2172,13 +2173,13 @@ void MHFloatingPointFrequencyTableBuilder::InitializeDomainBounds()
 			cout << KWContinuous::ContinuousToString(cUpperBound - GetMaxValue()) << "\t";
 			cout << dCost << "\t";
 			cout << dBestCost << "\t";
-			if (dCost < dBestCost)
+			if (dCost < dBestCost - dEpsilon)
 				cout << "Best";
 			cout << "\n";
 		}
 
 		// Memorisation si amelioration
-		if (dCost < dBestCost)
+		if (dCost < dBestCost - dEpsilon)
 		{
 			dBestCost = dCost;