diff --git a/cbor/src/main/java/com/fasterxml/jackson/dataformat/cbor/CBORParser.java b/cbor/src/main/java/com/fasterxml/jackson/dataformat/cbor/CBORParser.java
index dc52821d7..e342df939 100644
--- a/cbor/src/main/java/com/fasterxml/jackson/dataformat/cbor/CBORParser.java
+++ b/cbor/src/main/java/com/fasterxml/jackson/dataformat/cbor/CBORParser.java
@@ -777,13 +777,13 @@ protected void _releaseBuffers() throws IOException
     @Override
     public JsonToken nextToken() throws IOException
     {
-        _numTypesValid = NR_UNKNOWN;
         // For longer tokens (text, binary), we'll only read when requested
         if (_tokenIncomplete) {
             _skipIncomplete();
         }
         _tokenInputTotal = _currInputProcessed + _inputPtr;
         // also: clear any data retained so far
+        _numTypesValid = NR_UNKNOWN;
         _binaryValue = null;
 
         // First: need to keep track of lengths of defined-length Arrays and
@@ -1112,6 +1112,9 @@ protected JsonToken _handleTaggedBinary(TagList tags) throws IOException
         } else {
             // 12-May-2016, tatu: Since that's all we know, let's otherwise
             //   just return default Binary data marker
+            // 16-Jan-2024, tatu: Esoteric edge case where we have marked
+            //   `int` as being tokenized
+            _numTypesValid = NR_UNKNOWN;
             return (_currToken = JsonToken.VALUE_EMBEDDED_OBJECT);
         }
 
@@ -1558,7 +1561,7 @@ public String nextFieldName() throws IOException
             return name;
         }
         // otherwise just fall back to default handling; should occur rarely
-        return (nextToken() == JsonToken.FIELD_NAME) ? getCurrentName() : null;
+        return (nextToken() == JsonToken.FIELD_NAME) ? currentName() : null;
     }
 
     // 06-Apr-2023, tatu: Before Jackson 2.15, we had optimized variant, but
@@ -2224,6 +2227,11 @@ protected void convertNumberToBigDecimal() throws IOException
             // Let's parse from String representation, to avoid rounding errors that
             //non-decimal floating operations would incur
             final String text = getText();
+            // 16-Jan-2024, tatu: OSS-Fuzz managed to trigger this; let's fail
+            //   explicitly
+            if (text == null) {
+                _throwInternal();
+            }
             streamReadConstraints().validateFPLength(text.length());
             _numberBigDecimal = NumberInput.parseBigDecimal(
                     text, isEnabled(StreamReadFeature.USE_FAST_BIG_NUMBER_PARSER));
diff --git a/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/fuzz/CBORFuzz458_65768_NPETest.java b/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/fuzz/CBORFuzz458_65768_NPETest.java
new file mode 100644
index 000000000..814167f5b
--- /dev/null
+++ b/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/fuzz/CBORFuzz458_65768_NPETest.java
@@ -0,0 +1,41 @@
+package com.fasterxml.jackson.dataformat.cbor.fuzz;
+
+import com.fasterxml.jackson.core.JsonParser;
+import com.fasterxml.jackson.core.JsonToken;
+import com.fasterxml.jackson.core.exc.StreamReadException;
+
+import com.fasterxml.jackson.databind.ObjectMapper;
+
+import com.fasterxml.jackson.dataformat.cbor.CBORTestBase;
+
+public class CBORFuzz458_65768_NPETest extends CBORTestBase
+{
+    private final ObjectMapper MAPPER = cborMapper();
+
+    public void testInvalidText() throws Exception
+    {
+        final byte[] input = readResource("/data/clusterfuzz-cbor-65768.cbor");
+        try (JsonParser p = MAPPER.createParser(input)) {
+            try {
+                assertNull(p.nextTextValue());
+                assertToken(JsonToken.VALUE_NUMBER_FLOAT, p.currentToken());
+                assertEquals(0, p.getIntValue());
+                assertNull(p.nextTextValue());
+                assertNull(p.nextTextValue());
+                assertNull(p.nextTextValue());
+                assertNull(p.nextTextValue());
+                assertNull(p.nextTextValue());
+                assertNull(p.nextTextValue());
+                assertNull(p.nextTextValue());
+                assertNull(p.nextTextValue());
+                assertNull(p.nextTextValue());
+                assertToken(JsonToken.VALUE_EMBEDDED_OBJECT, p.currentToken());
+                p.getFloatValue();
+                p.getDecimalValue();
+                fail("Should not reach here (invalid input)");
+            } catch (StreamReadException e) {
+                verifyException(e, "Current token (VALUE_EMBEDDED_OBJECT) not numeric");
+            }
+        }
+    }
+}
diff --git a/cbor/src/test/resources/data/clusterfuzz-cbor-65768.cbor b/cbor/src/test/resources/data/clusterfuzz-cbor-65768.cbor
new file mode 100644
index 000000000..430ee0462
Binary files /dev/null and b/cbor/src/test/resources/data/clusterfuzz-cbor-65768.cbor differ
diff --git a/release-notes/CREDITS-2.x b/release-notes/CREDITS-2.x
index 463ae69ef..245bb7c84 100644
--- a/release-notes/CREDITS-2.x
+++ b/release-notes/CREDITS-2.x
@@ -303,3 +303,5 @@ Arthur Chan (@arthurscchan)
   (2.17.0)
  * Contributed #451: (cbor) `IndexOutOfBoundsException` in `CBORParser` for invalid input
   (2.17.0)
+ * Contributed #458: (cbor) Unexpected NullPointerException in `CBORParser`
+  (2.17.0)
diff --git a/release-notes/VERSION-2.x b/release-notes/VERSION-2.x
index a45d3a029..12dd3942f 100644
--- a/release-notes/VERSION-2.x
+++ b/release-notes/VERSION-2.x
@@ -35,6 +35,8 @@ Active maintainers:
  (fix contributed by Arthur C)
 #451: (cbor) `IndexOutOfBoundsException` in `CBORParser` for invalid input
  (fix contributed by Arthur C)
+#458: (cbor) Unexpected NullPointerException in `CBORParser`
+ (fix contributed by Arthur C)
 - (ion) Update `com.amazon.ion:ion-java` to 1.11.0 (from 1.10.5)
 
 2.16.1 (24-Dec-2023)