diff --git a/api.bs b/api.bs
index 3e8b23f..a4af595 100644
--- a/api.bs
+++ b/api.bs
@@ -984,36 +984,45 @@ defined in [[CLEAR-SITE-DATA#header]].
 
 When the [[CLEAR-SITE-DATA#clear-response|clear site data for response]] algorithm is invoked,
 if the list of types [=set/contains=] \``"impressions"`\`,
-the [=clear impressions for a conversion site=] is invoked,
+the [=clear impressions for a site=] is invoked,
 passing the <var ignore=''>origin</var>.
 
 <div algorithm>
-To <dfn>clear impressions for a conversion site</dfn>,
+To <dfn>clear impressions for a site</dfn>,
 given an [=origin=] |origin|,
 run these steps:
 
-1.  If |origin| is not a [=tuple origin=] with a [=scheme=] of `https`,
-    return.
+1.  If |origin| is not a [=tuple origin=], return.
 
 1.  Let |site| be the value returned
     by invoking [=registrable domain|obtain a registrable domain=],
-    passing the [=host=] part of the [=tuple origin|origin tuple=].
+    passing |origin|'s [=host=] part.
 
 1.  [=set/iterate|For each=] [=impression=] |impression| of
     the [=impression store=]:
 
+    1.  If |impression|'s [=impression/Intermediary Site=] is `undefined` and
+        its [=impression/Impression Site=] is equal to |site|,
+        [=set/remove=] |impression| from the [=impression store=] and [=iteration/continue=].
+
     1.  If |impression| has an [=impression/Intermediary Site=] equal to |site|,
         [=set/remove=] |impression| from the [=impression store=] and [=iteration/continue=].
 
-    1.  If |impression| has a [=impression/Conversion Sites=] [=set=]
-        that does not [=set/contain=] the value |site|, [=iteration/continue=].
+    1.  If |impression|'s [=impression/Conversion Sites=] [=set/contains=] |site|:
+
+        1.  [=set/Remove=] |site| from |impression|'s [=impression/Conversion Sites=].
+
+        1.  If |impression|'s [=impression/Conversion Sites=] [=set/is empty=],
+            [=set/remove=] |impression| from the [=impression store=] and
+            [=iteration/continue=].
+
+    1.  If |impression|'s [=impression/Conversion Callers=] [=set/contains=] |site|:
 
-    1.  If the [=set/size=] of |impression|'s [=impression/Conversion Sites=]
-        is greater than one,
-        [=set/remove|remove=] |site| from |impression|'s [=impression/Conversion Sites=]
-        and [=iteration/continue=].
+        1.  [=set/Remove=] |site| from |impression|'s [=impression/Conversion Callers=].
 
-    1.  Otherwise, [=set/remove=] |impression| from the [=impression store=].
+        1.  If |impression|'s [=impression/Conversion Callers=] [=set/is empty=],
+            [=set/remove=] |impression| from the [=impression store=] and
+            [=iteration/continue=].
 
 <p class=note>This process does not remove impressions
 that are saved with an empty [=set=] of [=impression/Conversion Sites=].
@@ -2873,7 +2882,7 @@ at the time they are saved.
 
 When clearing site data at the request of a [=site=],
 through the use of the [:Clear-Site-Data:] header,
-a [=user agent=] only [=clear impressions for a conversion site|removes impressions=],
+a [=user agent=] only [=clear impressions for a site|removes impressions=],
 without altering either the [=privacy budget store=]
 or the [=epoch start store=] for affected [=sites=].
 
diff --git a/impl/e2e-tests/clear-site-data.json b/impl/e2e-tests/clear-site-data.json
new file mode 100644
index 0000000..465204f
--- /dev/null
+++ b/impl/e2e-tests/clear-site-data.json
@@ -0,0 +1,245 @@
+{
+  "$comment": "use different advertiser sites to avoid depending on budgeting",
+  "events": [
+    {
+      "seconds": 1,
+      "site": "a.example",
+      "event": "saveImpression",
+      "options": { "histogramIndex": 0 }
+    },
+    {
+      "seconds": 2,
+      "site": "b.example",
+      "event": "saveImpression",
+      "options": {
+        "histogramIndex": 1,
+        "conversionSites": [
+          "advertiser-1.example",
+          "advertiser-2.example",
+          "advertiser-3.example"
+        ]
+      }
+    },
+    {
+      "seconds": 3,
+      "site": "c.example",
+      "intermediarySite": "d.example",
+      "event": "saveImpression",
+      "options": { "histogramIndex": 2 }
+    },
+    {
+      "seconds": 4,
+      "site": "advertiser-1.example",
+      "event": "measureConversion",
+      "$comment": "try to select 3 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 3,
+        "value": 6,
+        "maxValue": 6,
+        "credit": [1, 1, 1]
+      },
+      "expected": [2, 2, 2]
+    },
+    {
+      "seconds": 5,
+      "site": "c.example",
+      "event": "clearImpressionsForSite",
+      "$comment": "should remove no impressions, as although there is an impression site for c.example, it has a different intermediary site"
+    },
+    {
+      "seconds": 6,
+      "site": "advertiser-2.example",
+      "event": "measureConversion",
+      "$comment": "try to select 3 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 3,
+        "value": 6,
+        "maxValue": 6,
+        "credit": [1, 1, 1]
+      },
+      "expected": [2, 2, 2]
+    },
+    {
+      "seconds": 7,
+      "site": "d.example",
+      "event": "clearImpressionsForSite",
+      "$comment": "should remove only the impression with histogramIndex 2"
+    },
+    {
+      "seconds": 8,
+      "site": "advertiser-3.example",
+      "event": "measureConversion",
+      "$comment": "try to select 3 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 3,
+        "value": 6,
+        "maxValue": 6,
+        "credit": [1, 1, 1]
+      },
+      "expected": [3, 3, 0]
+    },
+    {
+      "seconds": 9,
+      "site": "advertiser-1.example",
+      "event": "clearImpressionsForSite",
+      "$comment": "should remove no impressions, but remove this site from the conversionSites of the impression with histogramIndex 1"
+    },
+    {
+      "seconds": 10,
+      "site": "advertiser-1.example",
+      "event": "measureConversion",
+      "$comment": "try to select 3 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 3,
+        "value": 6,
+        "maxValue": 6,
+        "credit": [1, 1, 1]
+      },
+      "expected": [6, 0, 0]
+    },
+    {
+      "seconds": 11,
+      "site": "advertiser-2.example",
+      "event": "clearImpressionsForSite",
+      "$comment": "should remove no impressions, but remove this site from the conversionSites of the impression with histogramIndex 1"
+    },
+    {
+      "seconds": 12,
+      "site": "advertiser-2.example",
+      "event": "measureConversion",
+      "$comment": "try to select 3 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 3,
+        "value": 6,
+        "maxValue": 6,
+        "credit": [1, 1, 1]
+      },
+      "expected": [6, 0, 0]
+    },
+    {
+      "seconds": 13,
+      "site": "advertiser-3.example",
+      "event": "clearImpressionsForSite",
+      "$comment": "should remove the impression with histogramIndex 1, as its conversion sites set should become empty"
+    },
+    {
+      "seconds": 14,
+      "site": "advertiser-3.example",
+      "event": "measureConversion",
+      "$comment": "try to select 3 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 3,
+        "value": 6,
+        "maxValue": 6,
+        "credit": [1, 1, 1]
+      },
+      "expected": [6, 0, 0]
+    },
+    {
+      "seconds": 15,
+      "site": "a.example",
+      "event": "clearImpressionsForSite",
+      "$comment": "should remove the impression with histogramIndex 0"
+    },
+    {
+      "seconds": 16,
+      "site": "advertiser-4.example",
+      "event": "measureConversion",
+      "$comment": "try to select 3 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 3,
+        "value": 6,
+        "maxValue": 6,
+        "credit": [1, 1, 1]
+      },
+      "expected": [0, 0, 0]
+    },
+    {
+      "seconds": 17,
+      "site": "e.example",
+      "event": "saveImpression",
+      "options": {
+        "histogramIndex": 3,
+        "conversionSites": ["advertiser-5.example"],
+        "conversionCallers": [
+          "intermediary-1.example",
+          "intermediary-2.example"
+        ]
+      }
+    },
+    {
+      "seconds": 18,
+      "site": "intermediary-1.example",
+      "event": "clearImpressionsForSite",
+      "$comment": "should remove no impressions, but remove this site from the conversionCallers of the impression with histogramIndex 3"
+    },
+    {
+      "seconds": 19,
+      "site": "advertiser-5.example",
+      "intermediarySite": "intermediary-1.example",
+      "event": "measureConversion",
+      "$comment": "try to select 4 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 4,
+        "value": 8,
+        "maxValue": 8,
+        "credit": [1, 1, 1, 1]
+      },
+      "expected": [0, 0, 0, 0]
+    },
+    {
+      "seconds": 20,
+      "site": "advertiser-5.example",
+      "intermediarySite": "intermediary-2.example",
+      "event": "measureConversion",
+      "$comment": "try to select 4 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 4,
+        "value": 8,
+        "maxValue": 8,
+        "credit": [1, 1, 1, 1]
+      },
+      "expected": [0, 0, 0, 8]
+    },
+    {
+      "seconds": 21,
+      "site": "intermediary-2.example",
+      "event": "clearImpressionsForSite",
+      "$comment": "should remove the impression with histogramIndex 3, as its conversion callers set should become empty"
+    },
+    {
+      "seconds": 22,
+      "site": "advertiser-5.example",
+      "intermediarySite": "intermediary-2.example",
+      "event": "measureConversion",
+      "$comment": "try to select 4 impressions to avoid depending on ordering",
+      "options": {
+        "aggregationService": "https://agg-service.example",
+        "epsilon": 0.5,
+        "histogramSize": 4,
+        "value": 8,
+        "maxValue": 8,
+        "credit": [1, 1, 1, 1]
+      },
+      "expected": [0, 0, 0, 0]
+    }
+  ]
+}
diff --git a/impl/src/backend.ts b/impl/src/backend.ts
index ebb95c2..1f67b03 100644
--- a/impl/src/backend.ts
+++ b/impl/src/backend.ts
@@ -18,7 +18,7 @@ interface Impression {
   impressionSite: string;
   intermediarySite: string | undefined;
   conversionSites: Set<string>;
-  conversionCallers: ReadonlySet<string>;
+  conversionCallers: Set<string>;
   timestamp: Temporal.Instant;
   lifetime: Temporal.Duration;
   histogramIndex: number;
@@ -601,19 +601,27 @@ export class Backend {
     return startEpoch;
   }
 
-  clearImpressionsForConversionSite(site: string): void {
+  clearImpressionsForSite(site: string): void {
     function shouldRemoveImpression(i: Impression): boolean {
-      if (i.intermediarySite === site) {
+      if (i.intermediarySite === undefined && i.impressionSite === site) {
         return true;
       }
-      if (!i.conversionSites.has(site)) {
-        return false;
+      if (i.intermediarySite === site) {
+        return true;
       }
-      if (i.conversionSites.size > 1) {
+      if (i.conversionSites.has(site)) {
         i.conversionSites.delete(site);
-        return false;
+        if (i.conversionSites.size === 0) {
+          return true;
+        }
       }
-      return true;
+      if (i.conversionCallers.has(site)) {
+        i.conversionCallers.delete(site);
+        if (i.conversionCallers.size === 0) {
+          return true;
+        }
+      }
+      return false;
     }
 
     this.#impressions = this.#impressions.filter(
diff --git a/impl/src/e2e.test.ts b/impl/src/e2e.test.ts
index 49e4350..c727c9a 100644
--- a/impl/src/e2e.test.ts
+++ b/impl/src/e2e.test.ts
@@ -19,11 +19,7 @@ interface TestCase {
   events: Event[];
 }
 
-type Event = {
-  seconds: number;
-  site: string;
-  intermediarySite?: string | undefined;
-} & (SaveImpression | MeasureConversion);
+type Event = SaveImpression | MeasureConversion | ClearImpressionsForSite;
 
 type ExpectedError =
   | "RangeError"
@@ -35,16 +31,28 @@ type ExpectedError =
 
 interface SaveImpression {
   event: "saveImpression";
+  seconds: number;
+  site: string;
+  intermediarySite?: string | undefined;
   options: AttributionImpressionOptions;
   expectedError?: ExpectedError;
 }
 
 interface MeasureConversion {
   event: "measureConversion";
+  seconds: number;
+  site: string;
+  intermediarySite?: string | undefined;
   options: AttributionConversionOptions;
   expected: number[] | ExpectedError;
 }
 
+interface ClearImpressionsForSite {
+  event: "clearImpressionsForSite";
+  seconds: number;
+  site: string;
+}
+
 function assertThrows(
   call: () => unknown,
   expectedError: ExpectedError,
@@ -137,6 +145,9 @@ function runTest(
 
         break;
       }
+      case "clearImpressionsForSite":
+        backend.clearImpressionsForSite(event.site);
+        break;
     }
   }
 }