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 d40df8bac..c686ef250 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
@@ -605,7 +605,7 @@ public JsonToken nextToken() throws IOException
                     _streamReadContext = _streamReadContext.getParent();
                     return (_currToken = JsonToken.END_OBJECT);
                 }
-                return (_currToken = _decodeFieldName());
+                return (_currToken = _decodePropertyName());
             }
         } else {
             if (!_streamReadContext.expectMoreValues()) {
@@ -1270,7 +1270,7 @@ public String nextTextValue() throws IOException
                     _currToken = JsonToken.END_OBJECT;
                     return null;
                 }
-                _currToken = _decodeFieldName();
+                _currToken = _decodePropertyName();
                 return null;
             }
         } else {
@@ -2557,7 +2557,7 @@ protected byte[] _finishLongContiguousBytes(final int expLen) throws IOException
         }
     }
 
-    protected final JsonToken _decodeFieldName() throws IOException
+    protected final JsonToken _decodePropertyName() throws IOException
     {     
         if (_inputPtr >= _inputEnd) {
             loadMoreGuaranteed();
@@ -3427,12 +3427,35 @@ protected void _handleEOF() throws JsonParseException {
         if (_streamReadContext.inRoot()) {
             return;
         }
-        String marker = _streamReadContext.inArray() ? "Array" : "Object";
-        _reportInvalidEOF(String.format(
-                ": expected close marker for %s (start marker at %s)",
-                marker,
-                _streamReadContext.getStartLocation(_ioContext.getSourceReference())),
-                null);
+        // Ok; end-marker or fixed-length Array/Object?
+        final JsonLocation loc = _streamReadContext.getStartLocation(_ioContext.getSourceReference());
+        final String startLocDesc = (loc == null) ? "[N/A]" : loc.sourceDescription();
+        if (_streamReadContext.hasExpectedLength()) { // specific length
+            final int expMore = _streamReadContext.getRemainingExpectedLength();
+            if (_streamReadContext.inArray()) {
+                _reportInvalidEOF(String.format(
+                        " in Array value: expected %d more elements (start token at %s)",
+                        expMore, startLocDesc),
+                        null);
+            } else {
+                _reportInvalidEOF(String.format(
+                        " in Object value: expected %d more properties (start token at %s)",
+                        expMore, startLocDesc),
+                        null);
+            }
+        } else {
+            if (_streamReadContext.inArray()) {
+                _reportInvalidEOF(String.format(
+                        " in Array value: expected an element or close marker (0xFF) (start token at %s)",
+                        startLocDesc),
+                        null);
+            } else {
+                _reportInvalidEOF(String.format(
+                        " in Object value: expected a property or close marker (0xFF) (start token at %s)",
+                        startLocDesc),
+                        null);
+            }
+        }
     }
 
     // Was "_handleCBOREOF()" before 2.13
diff --git a/cbor/src/main/java/com/fasterxml/jackson/dataformat/cbor/CBORReadContext.java b/cbor/src/main/java/com/fasterxml/jackson/dataformat/cbor/CBORReadContext.java
index 868b6d069..e490c04d6 100644
--- a/cbor/src/main/java/com/fasterxml/jackson/dataformat/cbor/CBORReadContext.java
+++ b/cbor/src/main/java/com/fasterxml/jackson/dataformat/cbor/CBORReadContext.java
@@ -138,7 +138,7 @@ public CBORReadContext createChildObjectContext(int expEntryCount)
     public int getRemainingExpectedLength() {
         int diff = _expEntryCount - _index;
         // Negative values would occur when expected count is -1
-        return Math.max(0, -diff);
+        return Math.max(0, diff);
     }
 
     public boolean acceptsBreakMarker() {
diff --git a/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/parse/ParseIncompleteArray240Test.java b/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/parse/ParseIncompleteArray240Test.java
new file mode 100644
index 000000000..3cf3ecb25
--- /dev/null
+++ b/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/parse/ParseIncompleteArray240Test.java
@@ -0,0 +1,73 @@
+package com.fasterxml.jackson.dataformat.cbor.parse;
+
+import com.fasterxml.jackson.core.JsonToken;
+import com.fasterxml.jackson.core.exc.StreamReadException;
+import com.fasterxml.jackson.dataformat.cbor.CBORFactory;
+import com.fasterxml.jackson.dataformat.cbor.CBORParser;
+import com.fasterxml.jackson.dataformat.cbor.CBORTestBase;
+
+public class ParseIncompleteArray240Test extends CBORTestBase
+{
+    private final CBORFactory F = cborFactory();
+
+    // [dataformats-binary#240]
+    public void testIncompleteFixedSizeArray() throws Exception
+    {
+        final byte[] input = {  (byte) 0x84 };
+        try (CBORParser p = cborParser(F, input)) {
+            assertToken(JsonToken.START_ARRAY, p.nextToken());
+            try {
+                p.nextToken();
+                fail("Should NOT pass");
+            } catch (StreamReadException e) {
+                verifyException(e, "Unexpected end-of-input in Array value: expected 4 more");
+            }
+        }
+    }
+
+    public void testIncompleteMarkerBasedArray() throws Exception
+    {
+        final byte[] input = {  (byte) 0x9F };
+        try (CBORParser p = cborParser(F, input)) {
+            assertToken(JsonToken.START_ARRAY, p.nextToken());
+            try {
+                p.nextToken();
+                fail("Should NOT pass");
+            } catch (StreamReadException e) {
+                verifyException(e, "Unexpected end-of-input in Array value: expected an element or ");
+            }
+        }
+    }
+
+    // And might as well do the same for Objects too
+    /*
+    public void testIncompleteFixedSizeObject() throws Exception
+    {
+        final byte[] input = {  (byte) 0xA3 };
+        try (CBORParser p = cborParser(F, input)) {
+            assertToken(JsonToken.START_OBJECT, p.nextToken());
+            try {
+                p.nextToken();
+                fail("Should NOT pass");
+            } catch (StreamReadException e) {
+                e.printStackTrace();
+                verifyException(e, "Unexpected end-of-input in Object value: expected 3 more");
+            }
+        }
+    }
+
+    public void testIncompleteMarkerBasedObject() throws Exception
+    {
+        final byte[] input = {  (byte) 0xBF };
+        try (CBORParser p = cborParser(F, input)) {
+            assertToken(JsonToken.START_OBJECT, p.nextToken());
+            try {
+                p.nextToken();
+                fail("Should NOT pass");
+            } catch (StreamReadException e) {
+                verifyException(e, "Unexpected end-of-input in Object value: expected an element or ");
+            }
+        }
+    }
+*/
+}
diff --git a/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/parse/ParseInvalidArray240Test.java b/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/parse/ParseInvalidArray240Test.java
deleted file mode 100644
index c98af6802..000000000
--- a/cbor/src/test/java/com/fasterxml/jackson/dataformat/cbor/parse/ParseInvalidArray240Test.java
+++ /dev/null
@@ -1,27 +0,0 @@
-package com.fasterxml.jackson.dataformat.cbor.parse;
-
-import com.fasterxml.jackson.core.JsonToken;
-import com.fasterxml.jackson.core.exc.StreamReadException;
-import com.fasterxml.jackson.dataformat.cbor.CBORFactory;
-import com.fasterxml.jackson.dataformat.cbor.CBORParser;
-import com.fasterxml.jackson.dataformat.cbor.CBORTestBase;
-
-public class ParseInvalidArray240Test extends CBORTestBase
-{
-    private final CBORFactory F = cborFactory();
-
-    // [dataformats-binary#240]
-    public void test1ByteIncompleteArray() throws Exception
-    {
-        final byte[] input = {  (byte) 0x84 };
-        try (CBORParser p = cborParser(F, input)) {
-            assertToken(JsonToken.START_ARRAY, p.nextToken());
-            try {
-                p.nextToken();
-                fail("Should NOT pass");
-            } catch (StreamReadException e) {
-                verifyException(e, "Unexpected end-of-input: expected close marker for Array");
-            }
-        }
-    }
-}