diff --git a/release-notes/VERSION-2.x b/release-notes/VERSION-2.x
index 34bbd09d50..5c29854ff0 100644
--- a/release-notes/VERSION-2.x
+++ b/release-notes/VERSION-2.x
@@ -14,6 +14,11 @@ a pure JSON library.
 === Releases ===
 ------------------------------------------------------------------------
 
+2.17.1 (not yet released)
+
+#1241: Fix `NumberInput.looksLikeValidNumber()` implementation
+ (contributed by @pjfanning)
+
 2.17.0 (12-Mar-2024)
 
 #507: Add `JsonWriteFeature.ESCAPE_FORWARD_SLASHES` to allow escaping of '/' for
diff --git a/src/main/java/com/fasterxml/jackson/core/io/NumberInput.java b/src/main/java/com/fasterxml/jackson/core/io/NumberInput.java
index 86c73a8986..bde9e32a63 100644
--- a/src/main/java/com/fasterxml/jackson/core/io/NumberInput.java
+++ b/src/main/java/com/fasterxml/jackson/core/io/NumberInput.java
@@ -39,7 +39,7 @@ public final class NumberInput
      * @since 2.17
      */
     private final static Pattern PATTERN_FLOAT = Pattern.compile(
-          "[+-]?[0-9]+(\\.[0-9]+)?([eE][+-]?[0-9]+)?");
+          "[+-]?[0-9]*[\\.]?[0-9]+([eE][+-]?[0-9]+)?");
 
     /**
      * Fast method for parsing unsigned integers that are known to fit into
@@ -570,6 +570,9 @@ public static BigInteger parseBigIntegerWithRadix(final String s, final int radi
      *<p>
      * Note: no trimming ({@code String.trim()}) nor null checks are performed
      * on String passed.
+     *<p>
+     * Note: this method returning {@code true} DOES NOT GUARANTEE String is valid
+     * number but just that it looks close enough.
      *
      * @param s String to validate
      *
@@ -578,6 +581,14 @@ public static BigInteger parseBigIntegerWithRadix(final String s, final int radi
      * @since 2.17
      */
     public static boolean looksLikeValidNumber(final String s) {
-        return (s != null) && PATTERN_FLOAT.matcher(s).matches();
+        // While PATTERN_FLOAT handles most cases we can optimize some simple ones:
+        if (s == null || s.isEmpty()) {
+            return false;
+        }
+        if (s.length() == 1) {
+            char c = s.charAt(0);
+            return (c <= '9') && (c >= '0');
+        }
+        return PATTERN_FLOAT.matcher(s).matches();
     }
 }
diff --git a/src/test/java/com/fasterxml/jackson/core/JUnit5TestBase.java b/src/test/java/com/fasterxml/jackson/core/JUnit5TestBase.java
index 983c4381cc..0a71c7d41e 100644
--- a/src/test/java/com/fasterxml/jackson/core/JUnit5TestBase.java
+++ b/src/test/java/com/fasterxml/jackson/core/JUnit5TestBase.java
@@ -9,7 +9,6 @@
 import com.fasterxml.jackson.core.testsupport.TestSupport;
 import com.fasterxml.jackson.core.testsupport.ThrottledInputStream;
 import com.fasterxml.jackson.core.testsupport.ThrottledReader;
-import org.junit.jupiter.api.Test;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
 import static org.junit.jupiter.api.Assertions.fail;
diff --git a/src/test/java/com/fasterxml/jackson/core/io/NumberInputTest.java b/src/test/java/com/fasterxml/jackson/core/io/NumberInputTest.java
index fbbad879d1..a84251eda3 100644
--- a/src/test/java/com/fasterxml/jackson/core/io/NumberInputTest.java
+++ b/src/test/java/com/fasterxml/jackson/core/io/NumberInputTest.java
@@ -7,7 +7,7 @@
 import static org.junit.jupiter.api.Assertions.*;
 
 class NumberInputTest
-        extends com.fasterxml.jackson.core.JUnit5TestBase
+    extends com.fasterxml.jackson.core.JUnit5TestBase
 {
     @Test
     void nastySmallDouble()
@@ -78,12 +78,24 @@ void looksLikeValidNumber()
         assertTrue(NumberInput.looksLikeValidNumber("0"));
         assertTrue(NumberInput.looksLikeValidNumber("1"));
         assertTrue(NumberInput.looksLikeValidNumber("-1"));
+        assertTrue(NumberInput.looksLikeValidNumber("+1")); // non-JSON
         assertTrue(NumberInput.looksLikeValidNumber("0001")); // non-JSON
 
+        // https://github.com/FasterXML/jackson-databind/issues/4435
+        assertTrue(NumberInput.looksLikeValidNumber(".0"));
+        assertTrue(NumberInput.looksLikeValidNumber(".01"));
+        assertTrue(NumberInput.looksLikeValidNumber("+.01"));
+        assertTrue(NumberInput.looksLikeValidNumber("-.01"));
+        assertTrue(NumberInput.looksLikeValidNumber("-.0"));
+
         assertTrue(NumberInput.looksLikeValidNumber("0.01"));
         assertTrue(NumberInput.looksLikeValidNumber("-0.10"));
         assertTrue(NumberInput.looksLikeValidNumber("+0.25")); // non-JSON
 
+        assertTrue(NumberInput.looksLikeValidNumber("10.33"));
+        assertTrue(NumberInput.looksLikeValidNumber("-1.39"));
+        assertTrue(NumberInput.looksLikeValidNumber("+125.0")); // non-JSON
+        
         assertTrue(NumberInput.looksLikeValidNumber("1E10"));
         assertTrue(NumberInput.looksLikeValidNumber("-1E10"));
         assertTrue(NumberInput.looksLikeValidNumber("1e-10"));
@@ -93,7 +105,10 @@ void looksLikeValidNumber()
         assertTrue(NumberInput.looksLikeValidNumber("1.4e+45"));
 
         assertFalse(NumberInput.looksLikeValidNumber(""));
+        assertFalse(NumberInput.looksLikeValidNumber(" "));
         assertFalse(NumberInput.looksLikeValidNumber("   "));
+        assertFalse(NumberInput.looksLikeValidNumber("."));
+        assertFalse(NumberInput.looksLikeValidNumber("0."));
         assertFalse(NumberInput.looksLikeValidNumber("10_000"));
     }
 }
diff --git a/src/test/java/com/fasterxml/jackson/core/read/TrailingCommasTest.java b/src/test/java/com/fasterxml/jackson/core/read/TrailingCommasTest.java
index afbb68413a..46be006277 100644
--- a/src/test/java/com/fasterxml/jackson/core/read/TrailingCommasTest.java
+++ b/src/test/java/com/fasterxml/jackson/core/read/TrailingCommasTest.java
@@ -17,9 +17,9 @@
 @SuppressWarnings("resource")
 public class TrailingCommasTest extends JUnit5TestBase {
 
-    private JsonFactory factory;
-    private Set<JsonReadFeature> features;
-    private int mode;
+    JsonFactory factory;
+    Set<JsonReadFeature> features;
+    int mode;
 
     public void initTrailingCommasTest(int mode, List<JsonReadFeature> features) {
       this.features = new HashSet<>(features);