diff --git a/tokio-bin-process/src/event_matcher.rs b/tokio-bin-process/src/event_matcher.rs
index 49ad20c..9c73fef 100644
--- a/tokio-bin-process/src/event_matcher.rs
+++ b/tokio-bin-process/src/event_matcher.rs
@@ -110,12 +110,17 @@ impl EventMatcher {
 
 /// Defines how many times the [`EventMatcher`] must match to pass an assertion.
 #[derive(Debug)]
+#[non_exhaustive]
 pub enum Count {
     /// This matcher must match this many times to pass an assertion.
     Times(usize),
     /// This matcher may match 0 or more times and will still pass an assertion.
     /// Use sparingly but useful for ignoring a warning or error that is not appearing deterministically.
     Any,
+    /// This matcher must match this many times or more to pass an asssertion
+    GreaterThanOrEqual(usize),
+    /// This matcher must match this many times or fewer to pass an asssertion
+    LessThanOrEqual(usize),
 }
 
 impl From<usize> for Count {
diff --git a/tokio-bin-process/src/process.rs b/tokio-bin-process/src/process.rs
index ca0f163..eb3d181 100644
--- a/tokio-bin-process/src/process.rs
+++ b/tokio-bin-process/src/process.rs
@@ -432,6 +432,16 @@ impl BinProcess {
                         panic!("Expected to find matches for {matcher:?}, {matcher_count} times but actually matched {count} times")
                     }
                 }
+                Count::GreaterThanOrEqual(x) => {
+                    if *count < x {
+                        panic!("Expected to find matches for {matcher:?}, greater than or equal to {x} times but actually matched {count} times")
+                    }
+                }
+                Count::LessThanOrEqual(x) => {
+                    if *count > x {
+                        panic!("Expected to find matches for {matcher:?}, less than or equal to {x} times but actually matched {count} times")
+                    }
+                }
             }
         }
     }