diff --git a/app/src/components/OutputsTable/OutputCell/OutputCell.tsx b/app/src/components/OutputsTable/OutputCell/OutputCell.tsx
index 50af4bd..f3da232 100644
--- a/app/src/components/OutputsTable/OutputCell/OutputCell.tsx
+++ b/app/src/components/OutputsTable/OutputCell/OutputCell.tsx
@@ -43,7 +43,7 @@ export default function OutputCell({
 
   type OutputSchema = Parameters<typeof provider.normalizeOutput>[0];
 
-  const { mutateAsync: hardRefetchMutate } = api.scenarioVariantCells.forceRefetch.useMutation();
+  const { mutateAsync: hardRefetchMutate } = api.scenarioVariantCells.hardRefetch.useMutation();
   const [hardRefetch, hardRefetching] = useHandledAsyncCallback(async () => {
     await hardRefetchMutate({ scenarioId: scenario.id, variantId: variant.id });
     await utils.scenarioVariantCells.get.invalidate({
diff --git a/app/src/server/api/routers/scenarioVariantCells.router.ts b/app/src/server/api/routers/scenarioVariantCells.router.ts
index 8e4c83b..ab677d1 100644
--- a/app/src/server/api/routers/scenarioVariantCells.router.ts
+++ b/app/src/server/api/routers/scenarioVariantCells.router.ts
@@ -61,7 +61,7 @@ export const scenarioVariantCellsRouter = createTRPCRouter({
         evalsComplete,
       };
     }),
-  forceRefetch: protectedProcedure
+  hardRefetch: protectedProcedure
     .input(
       z.object({
         scenarioId: z.string(),
@@ -85,7 +85,10 @@ export const scenarioVariantCellsRouter = createTRPCRouter({
       });
 
       if (!cell) {
-        await generateNewCell(input.variantId, input.scenarioId, { stream: true });
+        await generateNewCell(input.variantId, input.scenarioId, {
+          stream: true,
+          hardRefetch: true,
+        });
         return;
       }
 
@@ -96,7 +99,7 @@ export const scenarioVariantCellsRouter = createTRPCRouter({
         },
       });
 
-      await queueQueryModel(cell.id, true);
+      await queueQueryModel(cell.id, { stream: true, hardRefetch: true });
     }),
   getTemplatedPromptMessage: publicProcedure
     .input(
diff --git a/app/src/server/tasks/queryModel.task.ts b/app/src/server/tasks/queryModel.task.ts
index 081bc2c..750ac51 100644
--- a/app/src/server/tasks/queryModel.task.ts
+++ b/app/src/server/tasks/queryModel.task.ts
@@ -25,7 +25,6 @@ function calculateDelay(numPreviousTries: number): number {
 }
 
 export const queryModel = defineTask<QueryModelJob>("queryModel", async (task) => {
-  console.log("RUNNING TASK", task);
   const { cellId, stream, numPreviousTries } = task;
   const cell = await prisma.scenarioVariantCell.findUnique({
     where: { id: cellId },
@@ -153,7 +152,7 @@ export const queryModel = defineTask<QueryModelJob>("queryModel", async (task) =
           stream,
           numPreviousTries: numPreviousTries + 1,
         },
-        { runAt: retryTime, jobKey: cellId },
+        { runAt: retryTime, jobKey: cellId, priority: 3 },
       );
       await prisma.scenarioVariantCell.update({
         where: { id: cellId },
@@ -172,7 +171,13 @@ export const queryModel = defineTask<QueryModelJob>("queryModel", async (task) =
   }
 });
 
-export const queueQueryModel = async (cellId: string, stream: boolean) => {
+export const queueQueryModel = async (
+  cellId: string,
+  options: { stream?: boolean; hardRefetch?: boolean } = {},
+) => {
+  // Hard refetches are higher priority than streamed queries, which are higher priority than non-streamed queries.
+  const jobPriority = options.hardRefetch ? 0 : options.stream ? 1 : 2;
+
   await Promise.all([
     prisma.scenarioVariantCell.update({
       where: {
@@ -184,6 +189,13 @@ export const queueQueryModel = async (cellId: string, stream: boolean) => {
         jobQueuedAt: new Date(),
       },
     }),
-    queryModel.enqueue({ cellId, stream, numPreviousTries: 0 }, { jobKey: cellId }),
+
+    queryModel.enqueue(
+      { cellId, stream: options.stream ?? false, numPreviousTries: 0 },
+
+      // Streamed queries are higher priority than non-streamed queries. Lower
+      // numbers are higher priority in graphile-worker.
+      { jobKey: cellId, priority: jobPriority },
+    ),
   ]);
 };
diff --git a/app/src/server/tasks/runNewEval.task.ts b/app/src/server/tasks/runNewEval.task.ts
index 2da5ba4..83ae2e3 100644
--- a/app/src/server/tasks/runNewEval.task.ts
+++ b/app/src/server/tasks/runNewEval.task.ts
@@ -13,5 +13,6 @@ export const runNewEval = defineTask<RunNewEvalJob>("runNewEval", async (task) =
 });
 
 export const queueRunNewEval = async (experimentId: string) => {
-  await runNewEval.enqueue({ experimentId });
+  // Evals are lower priority than completions
+  await runNewEval.enqueue({ experimentId }, { priority: 4 });
 };
diff --git a/app/src/server/utils/generateNewCell.ts b/app/src/server/utils/generateNewCell.ts
index 678740d..b1221f9 100644
--- a/app/src/server/utils/generateNewCell.ts
+++ b/app/src/server/utils/generateNewCell.ts
@@ -9,10 +9,8 @@ import parsePromptConstructor from "~/promptConstructor/parse";
 export const generateNewCell = async (
   variantId: string,
   scenarioId: string,
-  options?: { stream?: boolean },
+  options: { stream?: boolean; hardRefetch?: boolean } = {},
 ): Promise<void> => {
-  const stream = options?.stream ?? false;
-
   const variant = await prisma.promptVariant.findUnique({
     where: {
       id: variantId,
@@ -121,6 +119,6 @@ export const generateNewCell = async (
       }),
     );
   } else {
-    await queueQueryModel(cell.id, stream);
+    await queueQueryModel(cell.id, options);
   }
 };