diff --git a/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs b/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
index 0ff3611f8f80..6e3e3b9b1448 100644
--- a/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
+++ b/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
@@ -536,7 +536,10 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
         // This helps us avoid overflow: see issue #72839
         // Since compilation is already guaranteed to fail, this is just
         // to try to show the 'nicest' possible errors to the user.
-        if obligation.references_error() {
+        // We don't check for errors in the `ParamEnv` - in practice,
+        // it seems to cause us to be overly aggressive in deciding
+        // to give up searching for candidates, leading to spurious errors.
+        if obligation.predicate.references_error() {
             return;
         }
 
diff --git a/src/test/ui/const-generics/generic_const_exprs/issue-72787.min.stderr b/src/test/ui/const-generics/generic_const_exprs/issue-72787.min.stderr
index 3a7095789336..02dce4f7a97e 100644
--- a/src/test/ui/const-generics/generic_const_exprs/issue-72787.min.stderr
+++ b/src/test/ui/const-generics/generic_const_exprs/issue-72787.min.stderr
@@ -1,5 +1,5 @@
 error: generic parameters may not be used in const operations
-  --> $DIR/issue-72787.rs:12:17
+  --> $DIR/issue-72787.rs:11:17
    |
 LL |     Condition<{ LHS <= RHS }>: True
    |                 ^^^ cannot perform const operation using `LHS`
@@ -8,7 +8,7 @@ LL |     Condition<{ LHS <= RHS }>: True
    = help: use `#![feature(generic_const_exprs)]` to allow generic const expressions
 
 error: generic parameters may not be used in const operations
-  --> $DIR/issue-72787.rs:12:24
+  --> $DIR/issue-72787.rs:11:24
    |
 LL |     Condition<{ LHS <= RHS }>: True
    |                        ^^^ cannot perform const operation using `RHS`
@@ -17,7 +17,7 @@ LL |     Condition<{ LHS <= RHS }>: True
    = help: use `#![feature(generic_const_exprs)]` to allow generic const expressions
 
 error: generic parameters may not be used in const operations
-  --> $DIR/issue-72787.rs:26:25
+  --> $DIR/issue-72787.rs:25:25
    |
 LL |     IsLessOrEqual<{ 8 - I }, { 8 - J }>: True,
    |                         ^ cannot perform const operation using `I`
@@ -26,7 +26,7 @@ LL |     IsLessOrEqual<{ 8 - I }, { 8 - J }>: True,
    = help: use `#![feature(generic_const_exprs)]` to allow generic const expressions
 
 error: generic parameters may not be used in const operations
-  --> $DIR/issue-72787.rs:26:36
+  --> $DIR/issue-72787.rs:25:36
    |
 LL |     IsLessOrEqual<{ 8 - I }, { 8 - J }>: True,
    |                                    ^ cannot perform const operation using `J`
@@ -35,15 +35,7 @@ LL |     IsLessOrEqual<{ 8 - I }, { 8 - J }>: True,
    = help: use `#![feature(generic_const_exprs)]` to allow generic const expressions
 
 error[E0283]: type annotations needed
-  --> $DIR/issue-72787.rs:10:38
-   |
-LL | impl<const LHS: u32, const RHS: u32> True for IsLessOrEqual<LHS, RHS> where
-   |                                      ^^^^ cannot infer type for struct `IsLessOrEqual<LHS, RHS>`
-   |
-   = note: cannot satisfy `IsLessOrEqual<LHS, RHS>: True`
-
-error[E0283]: type annotations needed
-  --> $DIR/issue-72787.rs:22:26
+  --> $DIR/issue-72787.rs:21:26
    |
 LL |     IsLessOrEqual<I, 8>: True,
    |                          ^^^^ cannot infer type for struct `IsLessOrEqual<I, 8_u32>`
@@ -51,13 +43,13 @@ LL |     IsLessOrEqual<I, 8>: True,
    = note: cannot satisfy `IsLessOrEqual<I, 8_u32>: True`
 
 error[E0283]: type annotations needed
-  --> $DIR/issue-72787.rs:22:26
+  --> $DIR/issue-72787.rs:21:26
    |
 LL |     IsLessOrEqual<I, 8>: True,
    |                          ^^^^ cannot infer type for struct `IsLessOrEqual<I, 8_u32>`
    |
    = note: cannot satisfy `IsLessOrEqual<I, 8_u32>: True`
 
-error: aborting due to 7 previous errors
+error: aborting due to 6 previous errors
 
 For more information about this error, try `rustc --explain E0283`.
diff --git a/src/test/ui/const-generics/generic_const_exprs/issue-72787.rs b/src/test/ui/const-generics/generic_const_exprs/issue-72787.rs
index 2ea5d634f6ef..77ad57f0640f 100644
--- a/src/test/ui/const-generics/generic_const_exprs/issue-72787.rs
+++ b/src/test/ui/const-generics/generic_const_exprs/issue-72787.rs
@@ -8,7 +8,6 @@ pub struct Condition<const CONDITION: bool>;
 pub trait True {}
 
 impl<const LHS: u32, const RHS: u32> True for IsLessOrEqual<LHS, RHS> where
-//[min]~^ ERROR type annotations needed
     Condition<{ LHS <= RHS }>: True
 //[min]~^ Error generic parameters may not be used in const operations
 //[min]~| Error generic parameters may not be used in const operations
diff --git a/src/test/ui/issues/issue-77919.rs b/src/test/ui/issues/issue-77919.rs
index 6e597b7669ab..966d76d148af 100644
--- a/src/test/ui/issues/issue-77919.rs
+++ b/src/test/ui/issues/issue-77919.rs
@@ -10,4 +10,4 @@ struct Multiply<N, M> {
 }
 impl<N, M> TypeVal<usize> for Multiply<N, M> where N: TypeVal<VAL> {}
 //~^ ERROR cannot find type `VAL` in this scope
-//~| ERROR type annotations needed
+//~| ERROR not all trait items implemented, missing: `VAL`
diff --git a/src/test/ui/issues/issue-77919.stderr b/src/test/ui/issues/issue-77919.stderr
index f98556bc72f4..97bd5ab36b65 100644
--- a/src/test/ui/issues/issue-77919.stderr
+++ b/src/test/ui/issues/issue-77919.stderr
@@ -17,15 +17,16 @@ LL | impl<N, M> TypeVal<usize> for Multiply<N, M> where N: TypeVal<VAL> {}
    |          |
    |          help: you might be missing a type parameter: `, VAL`
 
-error[E0283]: type annotations needed
-  --> $DIR/issue-77919.rs:11:12
+error[E0046]: not all trait items implemented, missing: `VAL`
+  --> $DIR/issue-77919.rs:11:1
    |
+LL |     const VAL: T;
+   |     ------------- `VAL` from trait
+...
 LL | impl<N, M> TypeVal<usize> for Multiply<N, M> where N: TypeVal<VAL> {}
-   |            ^^^^^^^^^^^^^^ cannot infer type for struct `Multiply<N, M>`
-   |
-   = note: cannot satisfy `Multiply<N, M>: TypeVal<usize>`
+   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ missing `VAL` in implementation
 
 error: aborting due to 3 previous errors
 
-Some errors have detailed explanations: E0283, E0412.
-For more information about an error, try `rustc --explain E0283`.
+Some errors have detailed explanations: E0046, E0412.
+For more information about an error, try `rustc --explain E0046`.