diff --git a/src/cargo/core/resolver/conflict_cache.rs b/src/cargo/core/resolver/conflict_cache.rs
index b35813bc35a..77f131a2581 100644
--- a/src/cargo/core/resolver/conflict_cache.rs
+++ b/src/cargo/core/resolver/conflict_cache.rs
@@ -35,9 +35,8 @@ pub(super) struct ConflictCache {
     // unconditionally true regardless of our resolution history of how we got
     // here.
     con_from_dep: HashMap<Dependency, Vec<HashMap<PackageId, ConflictReason>>>,
-    // `past_conflict_triggers` is an
-    // of `past_conflicting_activations`.
-    // For every `PackageId` this lists the `Dependency`s that mention it in `past_conflicting_activations`.
+    // `dep_from_pid` is an inverse-index of `con_from_dep`.
+    // For every `PackageId` this lists the `Dependency`s that mention it in `dep_from_pid`.
     dep_from_pid: HashMap<PackageId, HashSet<Dependency>>,
 }
 
@@ -62,6 +61,7 @@ impl ConflictCache {
         self.con_from_dep
             .get(dep)?
             .iter()
+            .rev() // more general cases are normally found letter. So start the search there.
             .filter(filter)
             .find(|conflicting| cx.is_conflicting(None, conflicting))
     }
diff --git a/tests/testsuite/resolve.rs b/tests/testsuite/resolve.rs
index 9ce7ccc4e42..99a3ccf0e6e 100644
--- a/tests/testsuite/resolve.rs
+++ b/tests/testsuite/resolve.rs
@@ -15,6 +15,13 @@ use support::resolver::{
 use proptest::collection::vec;
 use proptest::prelude::*;
 
+/// NOTE: proptest is a form of fuzz testing. It generates random input and makes shore that
+/// certain universal truths are upheld. Therefore, it can pass when there is a problem,
+/// but if it fails then there really is something wrong. When testing something as
+/// complicated as the resolver, the problems can be very subtle and hard to generate.
+/// We have had a history of these tests only failing on PRs long after a bug is introduced.
+/// If you have one of these test fail please report it on #6258,
+/// and if you did not change the resolver then feel free to retry without concern.
 proptest! {
     #![proptest_config(ProptestConfig {
         // Note that this is a little low in terms of cases we'd like to test,
@@ -34,6 +41,7 @@ proptest! {
         .. ProptestConfig::default()
     })]
 
+    /// NOTE: if you think this test has failed spuriously see the note at the top of this macro.
     #[test]
     fn passes_validation(
         PrettyPrintRegistry(input) in registry_strategy(50, 20, 60)
@@ -51,6 +59,7 @@ proptest! {
         }
     }
 
+    /// NOTE: if you think this test has failed spuriously see the note at the top of this macro.
     #[test]
     fn minimum_version_errors_the_same(
             PrettyPrintRegistry(input) in registry_strategy(50, 20, 60)
@@ -100,6 +109,7 @@ proptest! {
         }
     }
 
+    /// NOTE: if you think this test has failed spuriously see the note at the top of this macro.
     #[test]
     fn limited_independence_of_irrelevant_alternatives(
         PrettyPrintRegistry(input) in registry_strategy(50, 20, 60),
diff --git a/tests/testsuite/support/resolver.rs b/tests/testsuite/support/resolver.rs
index ae89eaf71f9..fd2a8d6f0ce 100644
--- a/tests/testsuite/support/resolver.rs
+++ b/tests/testsuite/support/resolver.rs
@@ -355,7 +355,7 @@ pub fn registry_strategy(
     max_versions: usize,
     shrinkage: usize,
 ) -> impl Strategy<Value = PrettyPrintRegistry> {
-    let name = string_regex("[A-Za-z_-][A-Za-z0-9_-]*(-sys)?").unwrap();
+    let name = string_regex("[A-Za-z][A-Za-z0-9_-]*(-sys)?").unwrap();
 
     let raw_version = [..max_versions; 3];
     let version_from_raw = |v: &[usize; 3]| format!("{}.{}.{}", v[0], v[1], v[2]);
@@ -460,12 +460,16 @@ pub fn registry_strategy(
 
 /// This test is to test the generator to ensure
 /// that it makes registries with large dependency trees
+///
+/// This is a form of randomized testing, if you are unlucky it can fail.
+/// A failure on it's own is not a big dael. If you did not change the
+/// `registry_strategy` then feel free to retry without concern.
 #[test]
 fn meta_test_deep_trees_from_strategy() {
     let mut dis = [0; 21];
 
     let strategy = registry_strategy(50, 20, 60);
-    for _ in 0..64 {
+    for _ in 0..128 {
         let PrettyPrintRegistry(input) = strategy
             .new_tree(&mut TestRunner::default())
             .unwrap()
@@ -488,19 +492,23 @@ fn meta_test_deep_trees_from_strategy() {
     }
 
     panic!(
-        "In 640 tries we did not see a wide enough distribution of dependency trees! dis: {:?}",
+        "In 1280 tries we did not see a wide enough distribution of dependency trees! dis: {:?}",
         dis
     );
 }
 
 /// This test is to test the generator to ensure
 /// that it makes registries that include multiple versions of the same library
+///
+/// This is a form of randomized testing, if you are unlucky it can fail.
+/// A failure on its own is not a big deal. If you did not change the
+/// `registry_strategy` then feel free to retry without concern.
 #[test]
 fn meta_test_multiple_versions_strategy() {
     let mut dis = [0; 10];
 
     let strategy = registry_strategy(50, 20, 60);
-    for _ in 0..64 {
+    for _ in 0..128 {
         let PrettyPrintRegistry(input) = strategy
             .new_tree(&mut TestRunner::default())
             .unwrap()
@@ -524,7 +532,7 @@ fn meta_test_multiple_versions_strategy() {
         }
     }
     panic!(
-        "In 640 tries we did not see a wide enough distribution of multiple versions of the same library! dis: {:?}",
+        "In 1280 tries we did not see a wide enough distribution of multiple versions of the same library! dis: {:?}",
         dis
     );
 }