diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8f1db8648..725db1877 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -13,6 +13,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 <a name="3.x"/>
 
 ## [Unreleased]
+### Fixed
+- Support records that don't allow 0 values in their fields, with Warning.ZERO_FIELDS. ([Issue 613](https://github.com/jqno/equalsverifier/issues/613))
 
 ## [3.9.1] - 2022-03-19
 ### Fixed
diff --git a/docs/_errormessages/record-failed-to-invoke-constructor.md b/docs/_errormessages/record-failed-to-invoke-constructor.md
new file mode 100644
index 000000000..e606415a5
--- /dev/null
+++ b/docs/_errormessages/record-failed-to-invoke-constructor.md
@@ -0,0 +1,32 @@
+---
+title: Record: failed to invoke constructor
+---
+    Record: failed to invoke constructor
+    If the record does not accept 0 as a value for its fields, consider providing valid prefab values for those fields and suppressing Warning.ZERO_FIELDS.
+
+Sometimes, a constructor needs to validate its input, throwing an exception on certain values. This can lead to problems when the value `0` is not allowed, and the constructor is part of a record instead of a regular class, like this:
+
+{% highlight java %}
+public record Foo(int i) {
+    public Foo {
+        if (i < 42) {
+            throw new IllegalArgumentException();
+        }
+    }
+}
+{% endhighlight %}
+
+One of the things EqualsVerifier does, is to run checks with fields set to their default values. For reference types, the default value is `null`, which has its own [chapter in the manual](/equalsverifier/manual/null). For primitive types, the default value is `0` (or `0.0`, `\u0000`, `false`). In regular classes, EqualsVerifier bypasses the constructor, so the exception can never be thrown. However, reflection support is much more limited for records, and their constructors cannot be bypassed.
+
+Therefore, we need to signal EqualsVerifier to skip the checks with default values, by suppressing `Warning.ZERO_FIELDS`.
+
+Another thing EqualsVerifier does, is to run checks with fields set to certain prefab values. For integral types, these values are `1` and `2`. If these values are not allowed by the record's constructor either, we need to provide new prefab values as well.
+
+In these cases, the call to EqualsVerifier will look like this:
+
+{% highlight java %}
+EqualsVerifier.forClass(Foo.class)
+        .suppress(Warning.ZERO_FIELDS)
+        .withPrefabValues(int.class, 42, 1337)
+        .verify();
+{% endhighlight %}
diff --git a/equalsverifier-core/src/main/java/nl/jqno/equalsverifier/internal/reflection/RecordObjectAccessor.java b/equalsverifier-core/src/main/java/nl/jqno/equalsverifier/internal/reflection/RecordObjectAccessor.java
index 8d93ba085..9deaf7010 100644
--- a/equalsverifier-core/src/main/java/nl/jqno/equalsverifier/internal/reflection/RecordObjectAccessor.java
+++ b/equalsverifier-core/src/main/java/nl/jqno/equalsverifier/internal/reflection/RecordObjectAccessor.java
@@ -141,7 +141,7 @@ private T callRecordConstructor(List<?> params) {
             () -> constructor.newInstance(params.toArray(new Object[0])),
             "Record: failed to invoke constructor.\n" +
             "  If the record does not accept 0 as a value for its fields," +
-            " consider providing valid prefab values for those fields and suppressing Warning.ZERO_FIELDS"
+            " consider providing valid prefab values for those fields and suppressing Warning.ZERO_FIELDS."
         );
     }
 }