diff --git a/release-notes/CREDITS-2.x b/release-notes/CREDITS-2.x
index a1f4986f69..66509e3785 100644
--- a/release-notes/CREDITS-2.x
+++ b/release-notes/CREDITS-2.x
@@ -231,3 +231,7 @@ Michel Feinstein (feinstein@github)
 Oleksandr Poslavskyi (alevskyi@github)
   * Contributed implementation of #504: Add a String Array write method in the Streaming API
   (2.11.0)
+
+James Agnew (jamesagnew@github)
+  * Contributed implementation of #611: Optionally allow leading decimal in float tokens
+  (2.11.0)
diff --git a/release-notes/VERSION-2.x b/release-notes/VERSION-2.x
index ccd4b16044..4ad508b587 100644
--- a/release-notes/VERSION-2.x
+++ b/release-notes/VERSION-2.x
@@ -25,6 +25,8 @@ JSON library.
 #606: Do not clear aggregated contents of `TextBuffer` when `releaseBuffers()` called
 #609: `FilteringGeneratorDelegate` does not handle `writeString(Reader, int)`
  (reported by Volkan Y)
+#611: Optionally allow leading decimal in float tokens
+ (contributed by James A)
 
 2.10.4 (not yet released)
 
diff --git a/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
index 3f423f6016..97004cece3 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
@@ -983,7 +983,6 @@ public Boolean nextBooleanValue() throws IOException
     /**********************************************************
      */
 
-
     // @since 2.11, [core#611]
     protected final JsonToken _parseFloatThatStartsWithPeriod() throws IOException
     {
@@ -992,9 +991,7 @@ protected final JsonToken _parseFloatThatStartsWithPeriod() throws IOException
             return _handleUnexpectedValue(INT_PERIOD);
         }
         char[] outBuf = _textBuffer.emptyAndGetCurrentSegment();
-        outBuf[0] = '.';
-        int c = _inputData.readUnsignedByte();
-        return _parseFloat(outBuf, 1, c, false, 0);
+        return _parseFloat(outBuf, 0, INT_PERIOD, false, 0);
     }
 
     /**
diff --git a/src/main/java/com/fasterxml/jackson/core/json/async/NonBlockingJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/async/NonBlockingJsonParser.java
index 3649674b30..297728fda4 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/async/NonBlockingJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/async/NonBlockingJsonParser.java
@@ -8,6 +8,7 @@
 import com.fasterxml.jackson.core.async.NonBlockingInputFeeder;
 import com.fasterxml.jackson.core.io.CharTypes;
 import com.fasterxml.jackson.core.io.IOContext;
+import com.fasterxml.jackson.core.json.JsonReadFeature;
 import com.fasterxml.jackson.core.sym.ByteQuadsCanonicalizer;
 import com.fasterxml.jackson.core.util.VersionUtil;
 
@@ -625,6 +626,13 @@ private final JsonToken _startValue(int ch) throws IOException
         // Should we have separate handling for plus? Although
         // it is not allowed per se, it may be erroneously used,
         // and could be indicate by a more specific error message.
+
+        case '.': // [core#611]
+            if (isEnabled(JsonReadFeature.ALLOW_LEADING_DECIMAL_POINT_FOR_NUMBERS.mappedFeature())) {
+                return _startFloatThatStartsWithPeriod();
+            }
+            break;
+
         case '0':
             return _startNumberLeadingZero();
         case '1':
@@ -1286,6 +1294,15 @@ protected JsonToken _reportErrorToken(String actualToken) throws IOException
     /**********************************************************************
      */
 
+    // [core#611]: allow non-standard floats like ".125"
+    protected JsonToken _startFloatThatStartsWithPeriod() throws IOException
+    {
+        _numberNegative = false;
+        _intLength = 0;
+        char[] outBuf = _textBuffer.emptyAndGetCurrentSegment();
+        return _startFloat(outBuf, 0, INT_PERIOD);
+    }
+    
     protected JsonToken _startPositiveNumber(int ch) throws IOException
     {
         _numberNegative = false;
diff --git a/src/test/java/com/fasterxml/jackson/failing/NonStandardNumbers611Test.java b/src/test/java/com/fasterxml/jackson/failing/NonStandardNumbers611Test.java
index c6109b72a5..b7736f97f5 100644
--- a/src/test/java/com/fasterxml/jackson/failing/NonStandardNumbers611Test.java
+++ b/src/test/java/com/fasterxml/jackson/failing/NonStandardNumbers611Test.java
@@ -6,6 +6,10 @@
 public class NonStandardNumbers611Test
     extends com.fasterxml.jackson.core.BaseTest
 {
+    private final JsonFactory JSON_F = JsonFactory.builder()
+            .enable(JsonReadFeature.ALLOW_LEADING_DECIMAL_POINT_FOR_NUMBERS)
+            .build();
+
     /**
      * The format ".NNN" (as opposed to "0.NNN") is not valid JSON, so this should fail
      */
@@ -22,10 +26,6 @@ public void testLeadingDotInDecimal() throws Exception {
         }
     }
 
-    private final JsonFactory JSON_F = JsonFactory.builder()
-            .enable(JsonReadFeature.ALLOW_LEADING_DECIMAL_POINT_FOR_NUMBERS)
-            .build();
-    
     public void testLeadingDotInDecimalAllowedAsync() throws Exception {
         _testLeadingDotInDecimalAllowed(JSON_F, MODE_DATA_INPUT);
     }