diff --git a/sim/tests/core.rs b/sim/tests/core.rs
index dc0b0a5..00f16c3 100644
--- a/sim/tests/core.rs
+++ b/sim/tests/core.rs
@@ -66,7 +66,7 @@
 
 /// These are the variants of dependencies we will test.
 pub static TEST_DEPS: &[DepTest] = &[
-    // First is a sanity test, no dependencies should upgrade.
+    // A sanity test, no dependencies should upgrade.
     DepTest {
         depends: [DepType::Nothing, DepType::Nothing],
         upgrades: [UpgradeInfo::Upgraded, UpgradeInfo::Upgraded],
@@ -98,6 +98,43 @@
         upgrades: [UpgradeInfo::Held, UpgradeInfo::Held],
     },
 
+    // Test where only the first image is upgraded, and there are no
+    // dependencies.
+    DepTest {
+        depends: [DepType::Nothing, DepType::NoUpgrade],
+        upgrades: [UpgradeInfo::Upgraded, UpgradeInfo::Held],
+    },
+
+    // Test one image with a valid dependency on the first image.
+    DepTest {
+        depends: [DepType::OldCorrect, DepType::NoUpgrade],
+        upgrades: [UpgradeInfo::Upgraded, UpgradeInfo::Held],
+    },
+
+    // Test one image with an invalid dependency on the first image.
+    DepTest {
+        depends: [DepType::Newer, DepType::NoUpgrade],
+        upgrades: [UpgradeInfo::Held, UpgradeInfo::Held],
+    },
+
+    // Test where only the second image is upgraded, and there are no
+    // dependencies.
+    DepTest {
+        depends: [DepType::NoUpgrade, DepType::Nothing],
+        upgrades: [UpgradeInfo::Held, UpgradeInfo::Upgraded],
+    },
+
+    // Test one image with a valid dependency on the second image.
+    DepTest {
+        depends: [DepType::NoUpgrade, DepType::OldCorrect],
+        upgrades: [UpgradeInfo::Held, UpgradeInfo::Upgraded],
+    },
+
+    // Test one image with an invalid dependency on the second image.
+    DepTest {
+        depends: [DepType::NoUpgrade, DepType::Newer],
+        upgrades: [UpgradeInfo::Held, UpgradeInfo::Held],
+    },
 ];
 
 /// Counter for the image number.