diff --git a/runtime/Java/src/org/antlr/v4/runtime/atn/ParserATNSimulator.java b/runtime/Java/src/org/antlr/v4/runtime/atn/ParserATNSimulator.java
index 5d3d05489..61ae46fff 100755
--- a/runtime/Java/src/org/antlr/v4/runtime/atn/ParserATNSimulator.java
+++ b/runtime/Java/src/org/antlr/v4/runtime/atn/ParserATNSimulator.java
@@ -798,6 +798,8 @@ public class ParserATNSimulator<Symbol extends Token> extends ATNSimulator {
 	public List<DFAState.PredPrediction> getPredicatePredictions(IntervalSet ambigAlts, SemanticContext[] altToPred) {
 		List<DFAState.PredPrediction> pairs = new ArrayList<DFAState.PredPrediction>();
 		int firstUnpredicated = ATN.INVALID_ALT_NUMBER;
+		// keep track of the position in pairs where the unpredicated choice should go
+		int firstUnpredicatedIndex = -1;
 		for (int i = 1; i < altToPred.length; i++) {
 			SemanticContext pred = altToPred[i];
 			// find first unpredicated but ambig alternative, if any.
@@ -809,6 +811,7 @@ public class ParserATNSimulator<Symbol extends Token> extends ATNSimulator {
 				 pred==SemanticContext.NONE && firstUnpredicated==ATN.INVALID_ALT_NUMBER )
 			{
 				firstUnpredicated = i;
+				firstUnpredicatedIndex = pairs.size();
 			}
 			if ( pred!=null && pred!=SemanticContext.NONE ) {
 				pairs.add(new DFAState.PredPrediction(pred, i));
@@ -817,7 +820,7 @@ public class ParserATNSimulator<Symbol extends Token> extends ATNSimulator {
 		if ( pairs.isEmpty() ) pairs = null;
 		else if ( firstUnpredicated!=ATN.INVALID_ALT_NUMBER ) {
 			// add default prediction if we found null predicate
-			pairs.add(new DFAState.PredPrediction(null, firstUnpredicated));
+			pairs.add(firstUnpredicatedIndex, new DFAState.PredPrediction(null, firstUnpredicated));
 		}
 //		System.out.println(Arrays.toString(altToPred)+"->"+pairs);
 		return pairs;
diff --git a/tool/test/org/antlr/v4/test/TestSemPredEvalParser.java b/tool/test/org/antlr/v4/test/TestSemPredEvalParser.java
index 5467c898a..7d0ed955f 100644
--- a/tool/test/org/antlr/v4/test/TestSemPredEvalParser.java
+++ b/tool/test/org/antlr/v4/test/TestSemPredEvalParser.java
@@ -105,11 +105,9 @@ public class TestSemPredEvalParser extends BaseTest {
 	}
 
 	@Test public void testOrder() throws Exception {
-		// Predicates disambiguate and so we don't arbitrarily choose the first alt
-		// Here, there are n-1 predicates for n=2 alts and so we simulate
-		// the nth predicate as !(others). We do that by testing the
-		// predicates first and then try the on predicated alternatives.
-		// Since the 2nd alternative has a true predicate, we always choose that one
+		// Under new predicate ordering rules (see antlr/antlr4#29), the first
+		// alt with an acceptable config (unpredicated, or predicated and evaluates
+		// to true) is chosen.
 		String grammar =
 			"grammar T;\n" +
 				"s : a {} a;\n" + // do 2x: once in ATN, next in DFA;
@@ -125,8 +123,8 @@ public class TestSemPredEvalParser extends BaseTest {
 		String found = execParser("T.g", grammar, "TParser", "TLexer", "s",
 								  "x y", false);
 		String expecting =
-			"alt 2\n" +
-			"alt 2\n";
+			"alt 1\n" +
+			"alt 1\n";
 		assertEquals(expecting, found);
 	}