diff --git a/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
index 1f64c9c8d3..193a08f1e1 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
@@ -777,11 +777,11 @@ public final JsonToken nextToken() throws IOException
             break;
 
         case '-':
-            t = _parsePossibleNumber(true);
+            t = _parseSignedNumber(true);
             break;
         case '+':
             if (isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
-                t = _parsePossibleNumber(false);
+                t = _parseSignedNumber(false);
             } else {
                 t = _handleOddValue(i);
             }
@@ -980,11 +980,11 @@ public String nextFieldName() throws IOException
 
         switch (i) {
         case '-':
-            t = _parsePossibleNumber(true);
+            t = _parseSignedNumber(true);
             break;
         case '+':
             if (isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
-                t = _parsePossibleNumber(false);
+                t = _parseSignedNumber(false);
             } else {
                 t = _handleOddValue(i);
             }
@@ -1059,11 +1059,11 @@ private final void _isNextTokenNameYes(int i) throws IOException
             _nextToken = JsonToken.VALUE_NULL;
             return;
         case '-':
-            _nextToken = _parsePossibleNumber(true);
+            _nextToken = _parseSignedNumber(true);
             return;
         case '+':
             if (isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
-                _nextToken = _parsePossibleNumber(false);
+                _nextToken = _parseSignedNumber(false);
             } else {
                 _nextToken = _handleOddValue(i);
             }
@@ -1104,11 +1104,11 @@ protected boolean _isNextTokenNameMaybe(int i, String nameToMatch) throws IOExce
         JsonToken t;
         switch (i) {
         case '-':
-            t = _parsePossibleNumber(true);
+            t = _parseSignedNumber(true);
             break;
         case '+':
             if (isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
-                t = _parsePossibleNumber(false);
+                t = _parseSignedNumber(false);
             } else {
                 t = _handleOddValue(i);
             }
@@ -1177,7 +1177,7 @@ private final JsonToken _nextTokenNotInObject(int i) throws IOException
             _matchToken("null", 1);
             return (_currToken = JsonToken.VALUE_NULL);
         case '-':
-            return (_currToken = _parsePossibleNumber(true));
+            return (_currToken = _parseSignedNumber(true));
             /* Should we have separate handling for plus? Although
              * it is not allowed per se, it may be erroneously used,
              * and could be indicated by a more specific error message.
@@ -1477,7 +1477,7 @@ private final JsonToken _parseFloat(int ch, int startPtr, int ptr, boolean neg,
         return resetFloat(neg, intLen, fractLen, expLen);
     }
 
-    private final JsonToken _parsePossibleNumber(final boolean negative) throws IOException
+    private final JsonToken _parseSignedNumber(final boolean negative) throws IOException
     {
         int ptr = _inputPtr;
         int startPtr = negative ? ptr-1 : ptr; // to include sign/digit already read
@@ -1493,7 +1493,7 @@ private final JsonToken _parsePossibleNumber(final boolean negative) throws IOEx
             if (ch == INT_PERIOD) {
                 return _parseFloatThatStartsWithPeriod();
             }
-            return _handleInvalidNumberStart(ch, negative);
+            return _handleInvalidNumberStart(ch, negative, true);
         }
         // One special case, leading zero(es):
         if (ch == INT_0) {
@@ -1722,6 +1722,11 @@ private char _verifyNLZ2() throws IOException
     // Method called if expected numeric value (due to leading sign) does not
     // look like a number
     protected JsonToken _handleInvalidNumberStart(int ch, boolean negative) throws IOException
+    {
+        return _handleInvalidNumberStart(ch, negative, false);
+    }
+
+    protected JsonToken _handleInvalidNumberStart(int ch, final boolean negative, final boolean hasSign) throws IOException
     {
         if (ch == 'I') {
             if (_inputPtr >= _inputEnd) {
@@ -1746,6 +1751,9 @@ protected JsonToken _handleInvalidNumberStart(int ch, boolean negative) throws I
                 _reportError("Non-standard token '"+match+"': enable `JsonReadFeature.ALLOW_NON_NUMERIC_NUMBERS` to allow");
             }
         }
+        if (!isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature()) && hasSign && !negative) {
+            reportUnexpectedNumberChar('+', "JSON spec does not allow numbers to have plus signs: enable `JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS` to allow");
+        }
         reportUnexpectedNumberChar(ch, "expected digit (0-9) to follow minus sign, for valid numeric value");
         return null;
     }
@@ -2026,7 +2034,7 @@ protected JsonToken _handleOddValue(int i) throws IOException
                     _reportInvalidEOFInValue(JsonToken.VALUE_NUMBER_INT);
                 }
             }
-            return _handleInvalidNumberStart(_inputBuffer[_inputPtr++], false);
+            return _handleInvalidNumberStart(_inputBuffer[_inputPtr++], false, true);
         }
         // [core#77] Try to decode most likely token
         if (Character.isJavaIdentifierStart(i)) {
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 b690b798fd..377b5e8ed8 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
@@ -1082,15 +1082,15 @@ protected JsonToken _parsePosNumber(int c) throws IOException
 
     protected final JsonToken _parsePosNumber() throws IOException
     {
-        return _parsePossibleNumber(false);
+        return _parseSignedNumber(false);
     }
 
     protected final JsonToken _parseNegNumber() throws IOException
     {
-        return _parsePossibleNumber(true);
+        return _parseSignedNumber(true);
     }
 
-    private final JsonToken _parsePossibleNumber(boolean negative) throws IOException
+    private final JsonToken _parseSignedNumber(boolean negative) throws IOException
     {
         char[] outBuf = _textBuffer.emptyAndGetCurrentSegment();
         int outPtr = 0;
@@ -1109,11 +1109,11 @@ private final JsonToken _parsePossibleNumber(boolean negative) throws IOExceptio
             } else if (c == INT_PERIOD) {
                 return _parseFloatThatStartsWithPeriod();
             } else {
-                return _handleInvalidNumberStart(c, negative);
+                return _handleInvalidNumberStart(c, negative, true);
             }
         } else {
             if (c > INT_9) {
-                return _handleInvalidNumberStart(c, negative);
+                return _handleInvalidNumberStart(c, negative, true);
             }
             c = _inputData.readUnsignedByte();
         }
@@ -2143,7 +2143,7 @@ protected JsonToken _handleUnexpectedValue(int c)
             _reportError("Non-standard token 'Infinity': enable `JsonReadFeature.ALLOW_NON_NUMERIC_NUMBERS` to allow");
             break;
         case '+': // note: '-' is taken as number
-            return _handleInvalidNumberStart(_inputData.readUnsignedByte(), false);
+            return _handleInvalidNumberStart(_inputData.readUnsignedByte(), false, true);
         }
         // [core#77] Try to decode most likely token
         if (Character.isJavaIdentifierStart(c)) {
@@ -2234,8 +2234,12 @@ protected JsonToken _handleApos() throws IOException
      * Method called if expected numeric value (due to leading sign) does not
      * look like a number
      */
-    protected JsonToken _handleInvalidNumberStart(int ch, boolean neg)
-        throws IOException
+    protected JsonToken _handleInvalidNumberStart(int ch, final boolean neg) throws IOException
+    {
+        return _handleInvalidNumberStart(ch, neg, false);
+    }
+
+    protected JsonToken _handleInvalidNumberStart(int ch, final boolean neg, final boolean hasSign) throws IOException
     {
         while (ch == 'I') {
             ch = _inputData.readUnsignedByte();
@@ -2253,6 +2257,9 @@ protected JsonToken _handleInvalidNumberStart(int ch, boolean neg)
             }
             _reportError("Non-standard token '"+match+"': enable `JsonReadFeature.ALLOW_NON_NUMERIC_NUMBERS` to allow");
         }
+        if (!isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature()) && hasSign && !neg) {
+            reportUnexpectedNumberChar('+', "JSON spec does not allow numbers to have plus signs: enable `JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS` to allow");
+        }
         reportUnexpectedNumberChar(ch, "expected digit (0-9) to follow minus sign, for valid numeric value");
         return null;
     }
diff --git a/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
index 61040ccb61..b749693898 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
@@ -812,11 +812,11 @@ public JsonToken nextToken() throws IOException
 
         switch (i) {
         case '-':
-            t = _parsePossibleNumber(true);
+            t = _parseSignedNumber(true);
             break;
         case '+':
             if (isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
-                t = _parsePossibleNumber(false);
+                t = _parseSignedNumber(false);
             } else {
                 t = _handleUnexpectedValue(i);
             }
@@ -885,12 +885,12 @@ private final JsonToken _nextTokenNotInObject(int i) throws IOException
             _matchNull();
             return (_currToken = JsonToken.VALUE_NULL);
         case '-':
-            return (_currToken = _parsePossibleNumber(true));
+            return (_currToken = _parseSignedNumber(true));
         case '+':
             if (!isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
                 return (_currToken = _handleUnexpectedValue(i));
             }
-            return (_currToken = _parsePossibleNumber(false));
+            return (_currToken = _parseSignedNumber(false));
         case '.': // [core#611]:
             return (_currToken = _parseFloatThatStartsWithPeriod());
         case '0':
@@ -1092,11 +1092,11 @@ public String nextFieldName() throws IOException
         JsonToken t;
         switch (i) {
         case '-':
-            t = _parsePossibleNumber(true);
+            t = _parseSignedNumber(true);
             break;
         case '+':
             if (isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
-                t = _parsePossibleNumber(false);
+                t = _parseSignedNumber(false);
             } else {
                 t = _handleUnexpectedValue(i);
             }
@@ -1220,11 +1220,11 @@ private final void _isNextTokenNameYes(int i) throws IOException
             _nextToken = JsonToken.VALUE_NULL;
             return;
         case '-':
-            _nextToken = _parsePossibleNumber(true);
+            _nextToken = _parseSignedNumber(true);
             return;
         case '+':
             if (isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
-                _nextToken = _parsePossibleNumber(false);
+                _nextToken = _parseSignedNumber(false);
             } else {
                 _nextToken = _handleUnexpectedValue(i);
             }
@@ -1287,11 +1287,11 @@ private final boolean _isNextTokenNameMaybe(int i, SerializableString str) throw
             t = JsonToken.VALUE_NULL;
             break;
         case '-':
-            t = _parsePossibleNumber(true);
+            t = _parseSignedNumber(true);
             break;
         case '+':
             if (isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature())) {
-                t = _parsePossibleNumber(false);
+                t = _parseSignedNumber(false);
             } else {
                 t = _handleUnexpectedValue(i);
             }
@@ -1503,7 +1503,7 @@ protected JsonToken _parsePosNumber(int c) throws IOException
         return resetInt(false, intLen);
     }
 
-    private final JsonToken _parsePossibleNumber(boolean negative) throws IOException
+    private final JsonToken _parseSignedNumber(boolean negative) throws IOException
     {
         char[] outBuf = _textBuffer.emptyAndGetCurrentSegment();
         int outPtr = 0;
@@ -1524,11 +1524,11 @@ private final JsonToken _parsePossibleNumber(boolean negative) throws IOExceptio
                 if (c == INT_PERIOD) {
                     return _parseFloatThatStartsWithPeriod();
                 }
-                return _handleInvalidNumberStart(c, negative);
+                return _handleInvalidNumberStart(c, negative, true);
             }
             c = _verifyNoLeadingZeroes();
         } else if (c > INT_9) {
-            return _handleInvalidNumberStart(c, negative);
+            return _handleInvalidNumberStart(c, negative, true);
         }
 
         // Ok: we can first just add digit we saw first:
@@ -2761,7 +2761,7 @@ protected JsonToken _handleUnexpectedValue(int c) throws IOException
                     _reportInvalidEOFInValue(JsonToken.VALUE_NUMBER_INT);
                 }
             }
-            return _handleInvalidNumberStart(_inputBuffer[_inputPtr++] & 0xFF, false);
+            return _handleInvalidNumberStart(_inputBuffer[_inputPtr++] & 0xFF, false, true);
         }
         // [core#77] Try to decode most likely token
         if (Character.isJavaIdentifierStart(c)) {
@@ -2870,7 +2870,12 @@ protected JsonToken _handleApos() throws IOException
 
     // Method called if expected numeric value (due to leading sign) does not
     // look like a number
-    protected JsonToken _handleInvalidNumberStart(int ch, boolean neg) throws IOException
+    protected JsonToken _handleInvalidNumberStart(int ch, final boolean neg) throws IOException
+    {
+        return _handleInvalidNumberStart(ch, neg, false);
+    }
+
+    protected JsonToken _handleInvalidNumberStart(int ch, final boolean neg, final boolean hasSign) throws IOException
     {
         while (ch == 'I') {
             if (_inputPtr >= _inputEnd) {
@@ -2894,6 +2899,9 @@ protected JsonToken _handleInvalidNumberStart(int ch, boolean neg) throws IOExce
             _reportError("Non-standard token '%s': enable `JsonReadFeature.ALLOW_NON_NUMERIC_NUMBERS` to allow",
                     match);
         }
+        if (!isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature()) && hasSign && !neg) {
+            reportUnexpectedNumberChar('+', "JSON spec does not allow numbers to have plus signs: enable `JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS` to allow");
+        }
         reportUnexpectedNumberChar(ch, "expected digit (0-9) to follow minus sign, for valid numeric value");
         return null;
     }
diff --git a/src/test/java/com/fasterxml/jackson/core/read/NonStandardNumberParsingTest.java b/src/test/java/com/fasterxml/jackson/core/read/NonStandardNumberParsingTest.java
index bcf6f662d3..1bd6aea0f8 100644
--- a/src/test/java/com/fasterxml/jackson/core/read/NonStandardNumberParsingTest.java
+++ b/src/test/java/com/fasterxml/jackson/core/read/NonStandardNumberParsingTest.java
@@ -37,14 +37,18 @@ public void testLeadingDotInDecimal() throws Exception {
      */
     public void testLeadingPlusSignInDecimal() throws Exception {
         for (int mode : ALL_MODES) {
-            JsonParser p = createParser(mode, " +123 ");
-            try {
+            try (JsonParser p = createParser(mode, " +123 ")) {
                 p.nextToken();
                 fail("Should not pass");
             } catch (JsonParseException e) {
-                verifyException(e, "expected digit (0-9) to follow minus sign, for valid numeric value");
+                verifyException(e, "Unexpected character ('+' (code 43)) in numeric value: JSON spec does not allow numbers to have plus signs: enable `JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS` to allow");
+            }
+            try (JsonParser p = createParser(mode, " +0.123 ")) {
+                p.nextToken();
+                fail("Should not pass");
+            } catch (JsonParseException e) {
+                verifyException(e, "Unexpected character ('+' (code 43)) in numeric value: JSON spec does not allow numbers to have plus signs: enable `JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS` to allow");
             }
-            p.close();
         }
     }