diff --git a/hibernate-core/src/main/java/org/hibernate/dialect/Dialect.java b/hibernate-core/src/main/java/org/hibernate/dialect/Dialect.java
index bd1e08cbbd..0d6bc2f5d4 100644
--- a/hibernate-core/src/main/java/org/hibernate/dialect/Dialect.java
+++ b/hibernate-core/src/main/java/org/hibernate/dialect/Dialect.java
@@ -2141,6 +2141,28 @@ public abstract class Dialect implements ConversionContext {
 		return false;
 	}
 
+	/**
+	 * For dropping a constraint with an "alter table", can the phrase "if exists" be applied before the constraint name?
+	 * <p/>
+	 * NOTE : Only one or the other (or neither) of this and {@link #supportsIfExistsAfterConstraintName} should return true
+	 *
+	 * @return {@code true} if the "if exists" can be applied before the constraint name
+	 */
+	public boolean supportsIfExistsBeforeConstraintName() {
+		return false;
+	}
+
+	/**
+	 * For dropping a constraint with an "alter table", can the phrase "if exists" be applied after the constraint name?
+	 * <p/>
+	 * NOTE : Only one or the other (or neither) of this and {@link #supportsIfExistsBeforeConstraintName} should return true
+	 *
+	 * @return {@code true} if the "if exists" can be applied after the constraint name
+	 */
+	public boolean supportsIfExistsAfterConstraintName() {
+		return false;
+	}
+
 	/**
 	 * Generate a DROP TABLE statement
 	 *
diff --git a/hibernate-core/src/main/java/org/hibernate/dialect/H2Dialect.java b/hibernate-core/src/main/java/org/hibernate/dialect/H2Dialect.java
index e085a9ba18..15b1c4d6c3 100644
--- a/hibernate-core/src/main/java/org/hibernate/dialect/H2Dialect.java
+++ b/hibernate-core/src/main/java/org/hibernate/dialect/H2Dialect.java
@@ -255,6 +255,11 @@ public class H2Dialect extends Dialect {
 		return true;
 	}
 
+	@Override
+	public boolean supportsIfExistsAfterConstraintName() {
+		return true;
+	}
+
 	@Override
 	public boolean supportsSequences() {
 		return true;
diff --git a/hibernate-core/src/main/java/org/hibernate/dialect/unique/DefaultUniqueDelegate.java b/hibernate-core/src/main/java/org/hibernate/dialect/unique/DefaultUniqueDelegate.java
index 4529760fd1..b65fa4e9bd 100644
--- a/hibernate-core/src/main/java/org/hibernate/dialect/unique/DefaultUniqueDelegate.java
+++ b/hibernate-core/src/main/java/org/hibernate/dialect/unique/DefaultUniqueDelegate.java
@@ -94,9 +94,17 @@ public class DefaultUniqueDelegate implements UniqueDelegate {
 			String defaultSchema) {
 		// Do this here, rather than allowing UniqueKey/Constraint to do it.
 		// We need full, simplified control over whether or not it happens.
-		final String tableName = uniqueKey.getTable().getQualifiedName( dialect, defaultCatalog, defaultSchema );
-		final String constraintName = dialect.quote( uniqueKey.getName() );
-		return "alter table " + tableName + " drop constraint " + constraintName;
+		final StringBuilder buf = new StringBuilder( "alter table " );
+		buf.append( uniqueKey.getTable().getQualifiedName( dialect, defaultCatalog, defaultSchema ) );
+		buf.append(" drop constraint " );
+		if ( dialect.supportsIfExistsBeforeConstraintName() ) {
+			buf.append( "if exists " );
+		}
+		buf.append( dialect.quote( uniqueKey.getName() ) );
+		if ( dialect.supportsIfExistsAfterConstraintName() ) {
+			buf.append( " if exists" );
+		}
+		return buf.toString();
 	}
 
 
diff --git a/hibernate-core/src/main/java/org/hibernate/mapping/ForeignKey.java b/hibernate-core/src/main/java/org/hibernate/mapping/ForeignKey.java
index 02caf61783..a36cf87a9d 100644
--- a/hibernate-core/src/main/java/org/hibernate/mapping/ForeignKey.java
+++ b/hibernate-core/src/main/java/org/hibernate/mapping/ForeignKey.java
@@ -127,10 +127,17 @@ public class ForeignKey extends Constraint {
 	}
 
 	public String sqlDropString(Dialect dialect, String defaultCatalog, String defaultSchema) {
-		return "alter table " + 
-			getTable().getQualifiedName(dialect, defaultCatalog, defaultSchema) + 
-			dialect.getDropForeignKeyString() + 
-			getName();
+		final StringBuilder buf = new StringBuilder( "alter table " );
+		buf.append( getTable().getQualifiedName(dialect, defaultCatalog, defaultSchema) );
+		buf.append( dialect.getDropForeignKeyString() );
+		if ( dialect.supportsIfExistsBeforeConstraintName() ) {
+			buf.append( "if exists " );
+		}
+		buf.append( getName() );
+		if ( dialect.supportsIfExistsAfterConstraintName() ) {
+			buf.append( " if exists" );
+		}
+		return buf.toString();
 	}
 
 	public boolean isCascadeDeleteEnabled() {